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Development of a Subcell Based Modeling Approach for Modeling the Architecturally Dependent Impact Response of Triaxially Braided Polymer Matrix Composites

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14
th
International LS-DYNA Users Conference
Session: Aerospace June 12-14, 2016
1-1
Development of a Subcell Based Modeling Approach for Modeling the Architecturally Dependent Impact Response of Triaxially Braided Polymer Matrix Composites
Christopher Sorini
1
, Aditi Chattopadhyay
1
, Robert K. Goldberg
2
, and Lee Kohlman
2
1
Arizona State University, Tempe, AZ, USA
2
NASA Glenn Research Center, Cleveland, OH, USA
Abstract
Understanding the high velocity impact response of polymer matrix composites with complex architectures is critical to many aerospace applications, including engine fan blade containment systems where the structure must be able to completely contain fan blades in the event of a blade-out. Despite the benefits offered by these materials, the complex nature of textile composites presents a significant challenge for the prediction of deformation and damage under both quasi-static and impact loading conditions. The relatively large mesoscale repeating unit cell (in comparison to the size of structural components) causes the material to behave like a structure rather than a homogeneous material. Impact experiments conducted at NASA Glenn Research Center have shown the damage patterns to be a function of the underlying material architecture. Traditional computational techniques that involve modeling these materials using smeared, homogeneous, orthotropic material properties at the macroscale result in simulated damage patterns that are a function of the structural geometry, but not the material architecture. In order to preserve heterogeneity at the highest length scale in a robust yet computationally efficient manner and capture the architecturally dependent damage patterns, a previously-developed subcell modeling approach is utilized. This work discusses the implementation of the subcell methodology into the commercial transient dynamic finite element code LS-DYNA
®
. Verification and validation studies are also presented, including simulating the tensile response of straight sided and notched quasi-static coupons composed of a T700/PR520 triaxially braided (0°/60°/
–
60°) composite. Based on the results of the verification and validation studies, advantages and limitations of the methodology and plans for future work are discussed.
Session: Aerospace
14
th
International LS-DYNA Users Conference
1-2
June 12-14, 2016
Introduction
Polymer matrix composites (PMCs) with complex textile architectures are increasingly being used by the aerospace industry in applications where impact resistance is critical, such as jet engine fan blade containment systems subjected to blade-out events. However, the complex nature of textile composites, particularly braided composites, presents a significant challenge for the prediction of the deformation and damage response of these structures, particularly under impact loading conditions. Experimental evidence has shown [1] that when these materials are subjected to impact, oftentimes the damage will propagate along fiber directions. This phenomenon is due to the relatively large repeating unit cell (RUC) in the braided composite as compared to the size of the composite structure [2]. Typically, modeling methodologies that have been developed to simulate the response of textile composites model the composite at the macroscopic scale as a smeared, orthotropic homogeneous material whereby only effective strength and stiffness properties are used [3]. However, when smeared homogeneous properties are used in numerical simulations to predict the initiation and propagation of damage, the damage patterns are merely functions of the structural geometry and the effects of the material architecture on the damage propagation are not properly accounted for [4]. To account for the effects of the composite architecture on the initiation and propagation of damage in a computationally efficient manner, a subcell-based approach has been developed in which the braided composite is approximated as a series of adjacent laminated composites [5-11]. The semi-analytical nature of this approach makes it both robust and computationally efficient. In this work, a critical evaluation and verification of this subcell methodology has been conducted. A number of simulations of straight-sided and notched tensile coupon tests have been conducted for a representative braided composite at a variety of different coupon orientations (0°, 30°, 60°, 90°). The results of the straight-sided coupon simulations are compared to those presented in Ref. 11 and the results of the notched coupon simulations are compared to experimental data.
Subcell Methodology
The subcell methodology consists of identifying the braided composite RUC and discretizing it into a series of unique subcell regions depending on the presence of axial and/or braider tows or lack thereof. In Figure 1(a), the red arrow denotes the direction of axial tows whereas the blue arrows denote the directions of the bias/braider tows in a triaxial braid. The current version of the subcell model has been designed to analyze triaxially braided composites with a [0º/60º/-60º] fiber architecture. Future efforts will involve generalizing the methodology such that other textile composite architectures can be simulated. The dimensions of the RUC are illustrated in Figure 1(b) and the unique subcells for the T700/PR520 material system are shown in Figure 1(c). It can be seen that subcells A and C are the only subcells with axial tows (red) whereas subcells B and D contain only braider tows (grey/black). Each subcell is then discretized through the thickness into an approximation of unidirectional (UD) plies, as depicted in Figure 1(d). The subcell discretization method shown in Figure 1(d) is known as the absorbed matrix model (AMM) due to the fact that instead of explicitly modeling layers of matrix, the braider plies are assumed to be a homogenized representation of the braider tows and surrounding matrix regions [10, 11]. Following this method, subcells A and C are modeled as asymmetric composite laminates and subcells B and D are modeled as symmetric composite laminates. The asymmetry
14
th
International LS-DYNA Users Conference
Session: Aerospace June 12-14, 2016
1-3 of subcells A and C allows the model to capture tension-twist coupling and local out-of-plane deformations when a specimen is loaded in tension [11].
Figure 1. Discretization process to generate subcell model.
Determination of Unidirectional Ply Thickness and Fiber Volume Fraction
Prior to the implementation of the subcell methodology into LS-DYNA [10], the appropriate geometric properties of the subcells must be determined. The approach described in Ref. 11 is used to determine the UD ply thicknesses and fiber volume fractions based on the geometric parameters presented in Table 1, which were determined in previous works by examining micrographs of the braided composite [5]. First the total volume of axial and/or braider fibers in subcells A/C and B/D are computed based on the fiber cross-sectional area, the number of fibers in each subcell, and the length of each of the axial/braider tows. The details of this process are described in Ref. 11. The lengths of the braider tows in subcells A/C and B/D are determined using the length, width, and height of the respective subcells and a straight-line assumption [8], in which the braider tows are approximated as a series of line segments; this is illustrated in Figure 2 and described in Ref. 8. Table 2 summarizes the calculated total volume of axial and braider fibers in each subcell.
Session: Aerospace
14
th
International LS-DYNA Users Conference
1-4
June 12-14, 2016
Table 1. Geometrical parameters used to determine unidirectional ply thicknesses and fiber volume fractions.
Parameter Description Value
W
A
Width of subcell A 4.201 mm W
B
Width of subcell B 4.765 mm H Height of RUC 0.56 mm V
tow
Fiber volume fraction of axial tows (assumed) 80% n
a
Number of fibers in axial tows 24k n
b
Number of fibers in braider tows 12k d
a
Diameter of axial tows
7 μm
d
b
Diameter of braider tows
7 μm
L Length of unit cell 5.1 mm
Θ
Braid angles +/-60°
Figure 2. Schematic of the straight-line model used to determine bias tow lengths. Table 2. Total volume of axial and braider fibers in each subcell.
Subcell Total Volume of Bias Fibers (m^3) Total Volume of Axial Fibers (m^3) A/C
4.48E-09 4.71E-09
B/D
5.11E-09 0
The thicknesses of the UD plies in subcell A/C are computed based on an assumed axial tow fiber volume fraction of 80% as well as the length, width, and height of subcells A/C [5]. Although this is not mentioned in Ref. 11, the thicknesses of the UD layers of subcells B/D are determined based on the assumption that there is an equal amount of plus and minus 60° braider tows present in subcells B/D. The next step is to determine the fiber volume fractions of the braider tows in subcells A/C and B/D. This is done using the procedure described in Ref. 11. The results obtained agree with those in Ref. 11 and are shown in Table 3. It is important to note that there are three unique fiber volume fractions (37.5%, 73.3%, and 80%) corresponding to three unique ply regions.

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