Reliability Based Design Optimization of Composite Joint Structures

Transcription

1 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<br>17th 4-7 May 2009, Palm Springs, California AIAA Reliability Based Design Optimization of Composite Joint Structures Galib Abumeri and Florent Rognin Alpha STAR Corporation, Long Beach, California USA Nasir Munir Northrop Grumman Corporation, El-Segundo, California USA Abstract This paper describes a computational simulation approach to maximize the durability, damage tolerance and reliability of composite joint structures in presence of material, fabrication and geometric uncertainties. This computer-based life prediction methodology combines composite mechanics with finite element analysis, damage and fracture tracking capability, probabilistic analysis and a robust design optimization algorithm to maximize reliability for given operating conditions. A naval composite joint [Ref 1] is assessed first with finite element based multi-scale progressive failure analysis to determine failure modes and locations as well as the fracture load. Design shape optimization is then used to maximize the joint durability without loss in reliability. The applied computational process ensures that certain type of failure modes, such as delamination progression, are contained to reduce risk to the structure. The design enhancement is achieved by minor tailoring of the shape of the structure to absorb the energy that induces delamination. The application of coupled optimization-probabilistic approach to naval joints shows that the structural reliability and durability can be simultaneously improved with little or no weight penalty. For the selected T joint example, durability using progressive failure analysis was performed and validated against test to determine the failure process: mechanisms, location, and load and to assess structural integrity. Next, robust design was performed with geometrical and material uncertainties. The reliability of the joint was improved from to with optimization resulting in a small weight increase, 1. 7%. The durability was also enhanced with robust design as the fracture load increased by 8% with optimization. Keywords: Durability and damage tolerance, Multi-Scale progressive failure analysis, Composite joint structures, delamination, robust design, reliability, probabilistic analysis. Copyright 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 1

2 1. Introduction Usage of polymer matrix composites (PMC) is rapidly increasing in the aerospace industry. T-joints in PMC aerospace components are attractive due to their light weight and relative low cost. Manufacturing costs are being dramatically reduced as automated fabrication processes evolve. To ensure quality joints it is important to quantify the level of joint structural safety under service load. According to Phillips and Shenoi [2] typical observed test failures are delamination initiation/growth in the T-joint overlay and cracks in the fillet region (Figure 1). In this study, alternative T-joint designs were evaluated to eliminate/minimize the observed test failure modes. Figure 2 shows the design parameters evaluated in this T-joint study. The relationship between damage evolution characteristics and remaining life needs to be established to permit in-service structural health monitoring of aircraft and engine structures. Figure 1. T-joint failures observed in test a) Alternative boundary angle attachment Figure 2. Alternative T-joint design approaches b) Joint design variables One objective of this study was to demonstrate the ability of the GENOA software package to accurately detect interlaminar failures in T-joints and compare the results with typical composite finite element analyses. The benchmark for this demonstration was Damage Tolerance of Laminated Tee Joints in FRP Structures (DTLTJ) [Ref. 2]. In this paper, a standard British Royal Navy radial T-joint was analyzed and compared to test data using progressive failure analysis in GENOA. Their results enabled a comparison between the GENOA analytical process and typical analysis methods involving high mesh density models and manual insertion of cracks and/or damage in order to model initiation and propagation of interlaminar failure mechanisms. The British Royal Navy radial T-joint (Figure 6) is used to transfer loads between two orthogonal members [Ref. 1, 3,4]. The joint is comprised of two PMC angles bonded to both sides of an upright plate member referred to as the web and then bonded to the base plate or flange. These angles or overlaminates form a boundary angle connection and are comprised of alternating polyester/e-glass woven roving (WR) and chopped strand mat (CSM) layers. The gap within the boundary angle is filled with a compatible resin. The gap area is referred to as the fillet. The members being joined are fabricated using polyester/e-glass woven roving. Three-point-bending test data on for theses joints was used to benchmark the analysis. The load-deflection curves for a typical test and loading conditions are depicted in Figure 3-a and 3-b for the load displacement. The simulation failure load and 2

3 displacement are close to those from test indicating that progressive failure analysis is a viable method to assess durability of the joint. Methods are needed to maximize performances using geometry updates and coupling parametric modeling to progressive failure analysis. A great advantage of such a method is that the user has the capability to quickly generate different shapes by changing the desired input values corresponding to geometric parameters. These parameters will be called design variables. Each set of geometry is then submitted for computation. This improves flexibility, ease of use and eventually reduces tests. This paper will focus on the following: 1) brief introduction to the methodology used in progressive damage analysis of composite joint structures, 2) probabilistic assessment of failure load due to scatter in constituent properties and manufacturing variables, 3) reliability based design methodology and 4) results and discussion Test Simulation Load (lbf) Deflection (in) (a) Configuration and laminate layups of (b) Load-displacement from Simulation and Test Naval composite joint Figure 3. Composite Joint Configuration and Load-Displacement Results 2.1. Progressive Fatigue Failure Analysis 2. Methodology PFA takes a full-scale finite element model and accounts for the average material failure at the microscopic level. Material properties are updated for each iteration reflecting any changes resulting from damage or crack propagation. The hierarchical approach (Figure 4) allows integration of a wide range of specialized programs, from micro to macro, into an existing verified progressive failure and probabilistic analysis tool [Ref. 3,4]. This makes it possible to accomplish synthesis of a variety of composite materials and structures based on progressive failure analysis and virtual testing to predict structure/component safety based on the physics and micro/macro mechanics of materials, manufacturing processes, available data, and service environments. This approach takes progressive damage and fracture processes into account and accurately assesses reliability and durability by predicting failure initiation and progression based on constituent material properties. 3

4 3D Fiber 2D Woven Vehicle Component FEM Traditional FEM stops here GENOA goes down to micro-scale Laminate Lamina Micro-Scale FEM results carried down to micro scale Sliced unit cell Reduced properties propagated up to vehicle scale Unit cell at node Figure 4. Hierarchical distribution of damage, stress, and strain from the macro to micro mechanical level. The life prediction code utilizes and integrates: (a) finite element structural analysis, (b) micro-mechanics, and fracture mechanics options, (c) damage progression tracking, (d) probabilistic risk assessment, (e) minimum damage design optimization, and (f) material characterization codes to scale up the effects of local damage mechanisms to the structure level to evaluate overall performance and integrity. A significant advantage of using a life prediction tool in the design process is that the number of experimental tests at the component and substructure levels can be substantially reduced and experimental testing that is done made more efficient and effective. The damage progression module relies on a composite mechanics code for composite micro-mechanics, macro-mechanics, laminate analysis, as well as cyclic loading durability analysis, and calls a finite element analysis module that uses anisotropic thick shell elements to model laminated composites. This capability predicts the loads where damage initiates and propagates, all the way to structural fracture Probabilistic Analysis With the direct coupling of composite micro-and-macro mechanics, structural analysis, and probabilistic methods [Ref. 5], it is possible to simulate uncertainties in all inherent scales of composites, from constituent materials to the whole structure and its loading conditions. The evaluation process starts with the identification of the primitive variables at the micro and macro composites scales including fabrication. These variables are selectively perturbed in order to generate a database for determining the relationships between the desired materials behavior and/or structural response and the primitive variables. The approach for probabilistic simulation is shown in Figure 5. Composite micro-mechanics are used to carry over the scatter in the primitive variables to the ply and laminate scales (Figure 5). Laminate theory is then used to determine the scatter in the material behavior at the laminate scale. This step leads to the perturbed resultant force/moment-displacement/curvature relationships used in the structural analysis. Next, the finite element analysis is performed to determine the perturbed structural responses corresponding to the selectively perturbed primitive variables. This completes the description of the hierarchical composite material/structure synthesis shown on the left side of Figure 5. The multi scale progressive decomposition of the structural response to the laminate, ply, and fiber-matrix constituent scales is shown on the right side of Figure 5. After the decomposition, the perturbed fiber, matrix, and ply stresses can be determined. 4

5 Figure 5. Technical approach for probabilistic evaluation of composite joints in GENOA 2.3. Reliability based design The generalized procedure for reliability based design optimization is presented in Figure 6. The process consists of deterministic shape optimization using a set of prescribed design variables (see Table 1 for joint design variables list and objective function). The technical effort focused on two types of joint loading: the first is the load that produces the first material failure (matrix cracking, delamination or fiber failure) and the second is the one that produces the total failure of joint (ultimate load). With the help of optimization, the load that produces the first material failure will be maximized subject to the following constraints: material damage volume, test ultimate load and targeted reliability. The optimization engine is based on the method of feasible directions [Ref. 5,6]. This method produces an improving succession of feasible design vectors by moving in a succession of usable directions. A feasible direction is one along which at least a small step can be taken without leaving the feasible domain and usable feasible direction is a feasible direction along which the objective function value can be minimized or maximized at least a small amount. For every new design predicted by optimization (that satisfies the load and damage constraints), probabilistic analysis is performed to assess the reliability of the new design. The probabilistic response function is the joint pull-off load that produces the first material damage. The random variables considered to exhibit uncertainties include fiber and matrix stiffness and strength and fiber and void volume ratio of the composite system. The authors seek to maximize the load that produces the first material failure while maintaining at least the same ultimate load from test (generally the ultimate load is higher than the load that produces the first damage as shown in Figure 3.b) subject to reliability constraints. 5

6 Figure 6. Technical Approach for Reliability Based Design Progressive failure analysis (PFA) is coupled with optimization and probabilistic methods [Ref 5,6] to derive an optimized shape of the joint while meeting reliability requirements. Sensitivity analysis is an effective tool to identify influential material and fabrication variables that produce scatter in the joint failure load. For the present case (See Table 1), the objective function is to maximize the reliability of the joint for given load. In order to achieve this, the initial geometry is updated by modifying the flange thickness/radius and the skin thickness in proportions that do not overweight the structure. Therefore, the weight is considered behavior constraint in this study. Next, deterministic results are discussed and presented followed by summary of optimization and reliability analysis. Table 1: List of Variables for Reliability Based Joint Design Shape Optimization Objective Function Optimization Design Variables Optimization Constraints Maximize the reliability of the joint for given design load. Flange thickness Flange radius Skin thickness Global weight of the structure 3. Results and Discussion A naval composite joint [Ref 1] is analyzed with progressive failure analysis. The failure load for the simply supported joint predicted by the analysis is about 8% lower than that of the test. The loaded joint and resulting load displacement relationship obtained from the analysis and compared to test are presented in Figures 3-a, and 3-b, 6

7 respectively. The composite joint, supported at the edges and loaded in the center, exhibited delamination in the flange region. The delamination initiation and propagation to fracture as predicted by the analysis is presented in Figure 7. Under increased loading, the joint stiffness is reduced because of the introduction of damage (that is evident by the load drop after it reached 1800 lb). Figure 7. Damage Progression as a Result of Increased Loading (Before Optimization) Structural Fracture at 3983 lb With an in-service load of 3500 lbf, the joint design reliability can be assessed and later improved using the combination of parametric tool for creating geometry/mesh and life prediction capabilities from GENOA. Table 2 summarizes the important results from the coupled optimization-reliability analysis. For an in-service load of 3500 lbf, the initial reliability equals to (39 failures per 1000). With optimization, the reliability is increased to (less than 5 failure per 1000 see Table 2-a). The optimized geometric parameters are: flange thickness, flange radius and skin thickness (Table 2-b). Global weight limits were also set. Thus, the flange thickness was reduced from to inch while the flange radius and the skin thickness were respectively increased from 1.0 to inch and from to inch. The global weight of the geometry was increased by 1.7% to get to the optimized shape of the joint. Finally, the uncertainties in the material and manufacturing processes are simulated by the standard deviations and probabilistic distributions in the material properties (Table 2- c) and processed through probabilistic analysis (before and after optimization). Table 2 : a) Objective function b) Design variables/constraint c) Probabilistic modeling for Reliability Based Joint Design Shape Optimization a) In-service load Objective Function Initial reliability Optimized reliability (lbf) b) Reliability Design Variable Initial value Optimized value Lower bound Upper bound Flange thickness (in) Flange radius (in) Skin thickness (in) Optimization Constraint Initial value Optimized value Lower bound Upper bound Weight (Lb) c) Random Variable Geometric Flange thickness (in) Mean value Coefficient of variation Standard deviation Distribution type % 1.07E-03 Normal 7

8 Flange radius (in) 1 2.5% 2.50E-02 Normal Skin thickness (in) % 1.07E-03 Normal Material Flange S11T (psi) % 1.15E+03 Normal Flange S33T (psi) % 5.10E+01 Normal Manufacturing Skin/web FVR Flange fiber misalignment ( ) % 2.30E-02 Normal 0 1% 1 Normal The probabilistic failure load as a result of the uncertainties described in Table 2 is presented in Figure 8 for material and fabrication random variables. For the initial joint a reliability of can be achieved when the load applied is less or equal to 3500 lb. The probabilistic analysis also shows that the probability that the maximum load is less or equal to 3100 lbf is 1/1,000. The cumulative probability that the load is less or equal to 4900 lbf is 999/1,000. For every one thousand joints made, very few will fail under a load of 3100 lbf and very few will fail when the load reaches or exceeds 4900 lbf. With the optimized model the reliability for 3500 lbf load is For this case, the scatter in the load ranged from 3400 lbf to 5300 lbf. It is evident that the reliability can be enhanced with just under 1.8% weight increase. Figure 8. Cumulative Distribution Function of maximum joint load Results presented in Figure 9.a) show that the flange radius has the greatest influence on the maximum load carrying capability of the structure, followed by the skin thickness and flange thickness. This was taken into account when assessing the geometric parameters of the optimized model to reduce the number of design variables. In Figure 9.b) the results indicate that the flange longitudinal/normal strength is the dominant uncertainty followed by the flange ply misalignment and the skin fiber volume ratio. 8

9 (a) (b) Figure 9. Probabilistic Sensitivities (before optimization) on the maximum joint load for a) geometric parameters and b) material properties In addition to the reliability improvement obtained from optimization, it is important to evaluate the joint performance from durability aspect as result of optimizing the geometry to maximize the reliability. Figure 10 presents the load displacement for the joint structure before and after optimization. One can conclude that the optimized structure increases the ultimate load by 8% as compared to the un-optimized one. The improved durability assures no growth in delamination as the load is increased. One important note to make here is that the load displacement before optimization is slightly different than the one presented in Figure 3. This is due to the fact during optimization, the authors relied on a parametric finite element model with one third the original mesh to expedite the computational process as it involves optimization and probabilistic analysis requiring large resources. Another benefit from the coupled optimization and probabilistic simulation is evident in the material damage volume percent plotted in Figure 11. Before optimization, the maximum material damage volume was 5.25%. With optimization, the damage sustained in the structure is reduced to 4.7% at the fracture load. That is a reduction of 11% in the total damage volume. It is the reduction in the damage volume that produced higher fracture load for the optimized structure. Information obtained from the robust design and probabilistic analysis is a powerful tool to improve the design and reliability of the structure and to reduce the number of tests needed for qualification and certification as long as it is possible to perform progressive failure analysis that is capable of depicting accurately the physical behavior of the structure. 9

10 Figure 10. Load Displacement Relationship Obtained from Progressive Failure Analysis Before and After Optimizing the Joint Structure Figure 11. Material Damage Volume as a Result of Applied Loading Obtained from Progressive Failure Analysis Before and After Optimizing the Joint Structure 4. Conclusions An advanced methodology for enhancing the reliability of complex composite joint structures was demonstrated. The method is a judicious combination of composite micro and macro mechanics, finite element, durability and damage tolerance, robust optimization and probabilistic methods. The following can be concluded from the present study: 1) Flange geometry and strength are key variables that drive the delamination and fracture in the joint. 1

11 2) Reliability is improved with optimization from to ) Fracture load is increased by 8% with optimization sustaining less damage than before optimization. 4) Ability to parametrically update the analysis model during coupled optimization and probabilistic analysis improves the efficiency of the computational process. 5) Information obtained from the probabilistic sensitivity analysis can be used as an effective guide during a test program by identifying influential variables on the design of the composite joints. 6) The methodology is versatile and applicable to all structures, especially where data is difficult to obtain. References 1 K.T. Kedward, and R.S. Wilson, et al Flexure of simply curved composite shapes, Composite Volume 20, November H.J. Phillips, and R.A. Shenoi., Damage Tolerance of Laminated Tee Joints in FRP Structures, Composites Part A Applied Science and Manufacturing, Vol. 29, No. 4, pp. 465, F. Abdi, T. Castillo, D. Huang, V. Chen, A. Del Mundo Virtual Testing of the X37 Space Vehicle. SAMPE Conference Paper C. Godines, F. Abdi, S. Kiefer, K. Kedward Simplified Analytical Procedure for Prediction of Fracture Damage in Composite Structures. ASTM Conference Paper 3/17/03. 5 G. Abumeri, F. Abdi, M. Baker, M. Triplet, and J. Griffin, Reliability Based Design of Composite Over- Wrapped Tanks, SAE World Congress, F. Abdi, Z. Qian, and M. Lee, The Premature Failure of 3D Woven Composites, ACMA Composites 2005, Columbus, Ohio, September 28-30,