E.C. Colley and D.M. Sabados, Rotorcraft Systems Engineering and Simulation Center, University of Alabama in Huntsville

INTRODUCTION:

Damage tolerance analysis of composite materials has historically been very difficult to perform. The maturity level of approaches within the aerospace community is low; therefore, damage tolerance analysis techniques are often supplemented with carefully planned testing to substantiate the results generated via analysis. The University of Alabama in Huntsville (UAH) has been conducting research into the damage tolerance of unidirectional fiberglass materials typically used in aerospace flight vehicle structures. The first phase of this project included the development of an analytical approach (using MSC/NASTRAN) to investigate the damage tolerance of wrinkled laminated structures.

TYPES OF DAMAGE:

Laminated composite structures are routinely being used in aerospace structures. Large co-cured structures are being fabricated that use a variety of tooling and mold configurations. These types of structures yield very safe, structurally efficient, and lightweight components such as airframes, missile primary structures, and rotorcraft blades. Flight critical structures such as these are designed to maintain excellent damage tolerance and provide long life after failure indication.

During the fabrication process, manufacturing-related defects, manifesting in the form of wrinkles, can be introduced into the laminated structure, as depicted in Figure 1. These wrinkles can have a wide variety of shapes and sizes and often result in reduced strength and lower fatigue life of the material. As shown in Figure 1, the fiber distortion is comprised of a wide variety of damage mechanisms including fiber breakage, fiber void areas, resin rich areas, and matrix cracking. Typically, these damaged areas are located below the surface of the laminate and are therefore very difficult to inspect using conventional non-destructive evaluation (NDE) techniques.

The amount of crack propagation emanating from these distorted areas is highly dependent on the initial crack geometry and the orientation of the crack relative to the applied loads. When it comes to fatigue loading, aerospace composite structures are often subjected to a "no-growth" crack criterion. In other words, manufacturing flaws such as wrinkled composites and barely visible impact damage (BVID) are not permitted to grow within the structure. This generally leads to components being pulled from service that have a substantial amount of useful fatigue life, putting an unwanted burden on the user of the system. Therefore, viable damage tolerance analysis techniques must have the ability to capture fatigue crack growth over all regions of crack growth rates and orientations. The fracture toughness for the mode-I crack shown in Figure 2 is much lower than a mode-II and mode-III crack. Therefore, if the crack is oriented in such a way that mode-II and mode-III are the dominating loads, it is feasible that the crack could have a copious amount of life. On the other hand, a mode-I crack could grow much faster than anticipated, resulting in premature failure of the structure.

The challenge of performing a damage tolerance analysis on hardware in the condition depicted in Figure 1 is that the structure contains three-dimensional defects. Fiber breakage, fiber void areas, and matrix cracking present a 3-D path for the crack to grow. Knowledge of the crack initial conditions and orientation is often very difficult to determine given the limited amount of information provided by industry standard NDE techniques such as radiography and ultrasonic. As a result, UAH researchers focused on evaluating damage tolerance approaches that could account for the unknown crack initial conditions and conservatively calculate the crack growth direction, shape, and length after a given number of load cycles. Of all of the approaches evaluated by UAH, including displacement compatibility models, cohesive models, linearized 3-D failure criteria, and other energy release rate failure models, the Virtual Crack Closure Technique (VCCT) has the capability and flexibility to accurately and/or conservatively calculate the damage tolerance of wrinkled laminate composites.

VCCT APPROACH WITH MSC SOFTWARE:

UAH conducted an enormous amount of research into VCCT covering 1987 to the present day. During the review process, UAH evaluated several aspects of the technique pertinent to composite structures and defects similar to those depicted in Figure 1. Aspects including 2-D and 3-D modeling techniques, methodologies for computing the strain energy release rate (SERR), fatigue and damage tolerance methodologies, and SERR testing methods were all evaluated by UAH researchers. Of all of the damage tolerance methods evaluated by UAH, the VCCT method was chosen because its heritage and foundation is based on common aerospace practices that have been used for decades to calculate fatigue crack growth in flight hardware.

Over the last few years, the VCCT has been implemented into finite element methods (e.g. MSC/NASTRAN and MSC/MARC) because it eliminates the analytical problems that arise with stress singularities at the crack tip. One of the other reasons the VCCT has gained acceptance within the aerospace industry is because the strain energy release rate is proportional to the fracture toughness. Therefore, the critical variables associated with the technique can be measured during simple couple level material testing.

The VCCT is based on the hypothesis that the energy released by a crack is the same as the work required to close the crack. To briefly explain the VCCT methodology, consider a crack approaching from the left under a pure mode-I load condition where the crack tip is located at nodes (2,5), as shown in Figure 3. The mode-I strain energy release rate (GI) is calculated using the grid point forces between nodes (2,5) and the relative displacement between nodes (1,6). Similar calculations can be made to determine the mode-II and mode-III strain energy release rates. The strain energy release rate is compared to the critical strain energy (GIC) which dictates whether the energy is sufficient to grow the crack. Given the dimensional spacing of the nodes in the vicinity of the crack tip, the result of the fatigue life is the number of cycles required to release the element and grow the crack.

UAH conducted several evaluations of the VCCT with the MSC/NASTRAN and MSC/MARC solvers. Both MSC/NASTRAN and MSC/MARC are general purpose finite element solvers that have the ability to solve large nonlinear geometric problems such as fatigue crack growth in a given material. There are certain key aspects of the VCCT that UAH evaluated, namely glued contact, released glued contact, Paris equation crack growth, and crack growth via re-meshing.

To evaluate the glued contact and released glued contact features, UAH developed a finite element model of a simple material coupon, as shown in Figure 4. The finite element model contained 80,091 CHEXA solid elements and 71,380 grid points. The plate was separated into two halves and "glued" together using a contact boundary condition. The VCCT uses glued contact boundary conditions to release elements as the crack growths along a given path. The VCCT was used to calculate the strain energy release rate and release the glued contact along the crack front. As shown in the figure, the crack front is through the thickness of the material and remains that way throughout the solution. The analysis shown in Figure 4 demonstrates the ability of the VCCT to release glued contact elements as a function of strain energy release rate.

The evaluations conducted by UAH have provided valuable information on the VCCT and the various conditions that must exist to utilize this method for the damage tolerance analysis of complex aerospace structures. As previously mentioned, the VCCT was just recently added to mainstream finite element solvers. As such, there are improvements that can be made to aid in the solution. As this project progresses, UAH will work with the software developers to enhance these solutions to make them more user friendly and compliant with standard aerospace practices regarding damage tolerance analysis. UAH has already provided some suggestions along these lines, and MSC Software Corporation is amenable to updating their software products to meet the needs of the damage tolerance community. UAH and MSC Software Corporation are in agreement that the VCCT foundation has already been well established, and the only changes that are needed relate to simple material properties and cyclic loading inputs.

MATERIAL PROPERTY TESTING:

UAH researchers are currently developing test plans to generate the fracture toughness data needed to verify the VCCT approach and test-correlate the finite element models used in the analysis. The tests listed below will be conducted on fiberglass materials that are common within the aerospace community. MSC software products will be used to perform pre-test predictions and post-test correlation of the data. The data generated during these tests and the analytical methods derived from the correlation activities will provide the damage tolerance community with a test verified approach to estimate the crack growth behavior in fiber reinforced polymer matrix composite structures.

  1. MODE-I INTERLAMINAR FRACTURE TOUGHNESS TEST
    Determine the opening mode-I interlaminar fracture toughness and the number of cycles (N) for the onset of delamination growth using a Double Cantilever Beam (DCB) specimen.
  2. MODE-I TRANSLAMINAR FRACTURE TOUGHNESS TEST
    Determine the opening mode-I translaminar fracture toughness and the number of cycles for the onset of fatigue crack growth using an eccentrically loaded notched specimen.
  3. MIXED MODE I/II INTERLAMINAR FRACTURE TOUGHNESS TEST
    Determine the interlaminar fracture toughness at various mode-I and mode-II loading ratios using a Mixed Mode Bending (MMB) specimen.
  4. WRINKLED - MODE I INTERLAMINAR FRACTURE TOUGHNESS TEST
    Determine the opening mode-I interlaminar fracture toughness and the number of cycles for the onset of delamination growth using a wrinkled DCB specimen.
  5. WRINKLED - MODE I TRANSLAMINAR FRACTURE TOUGHNESS TEST
    Determine the opening mode-I translaminar fracture toughness and the number of cycles for the onset of fatigue crack growth using a wrinkled eccentrically loaded notched specimen.