Multiphysics Simulation of Process Induced Deformations in Polymer Matrix Composites

Transcription

1 Multiphysics Simulation of Process Induced Deformations in Polymer Matrix Composites Taha S. Khot 1, Vinayak Khandare 1,2, Jitesh Vasavada 1, K. P. Desai 2 and Asim Tewari 3 1 National Centre for Aerospace Innovation & Research (NCAIR), Indian Institute of Technology Bombay, Mumbai , INDIA 2 Department of Mechanical Engineering, Sardar Vallabhbhai Patel National Institute of Technology, Surat , INDIA 3 Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai , INDIA Abstract Generation of residual stresses is a phenomenon that occurs during autoclave processing of thermoset polymer matrix composite structures. Such stresses lead to process induced deformations (PID) such as spring-in, warpage, and shrinkage of composite parts. The PID results in poor dimensional fidelity of composite parts, thereby, leading to increased costs and manufacturing delays. This paper studies these deformations by performing numerical multi-physics simulation of cure kinetics, heat transfer, and stress analysis. The simulations have been performed for a set angled components, such as L- and C-Sections. It is found that there is huge difference in the stresses at the bottom and at the top plies of the composite, at the end of the autoclaving process. These residual stresses are the main cause for the springin deformation of the composite after tool-removal. Further, it is seen that altering the tool geometry to compensate for the spring-in can significantly improve the dimensional fidelity of the final composite part. 1.0 INTRODUCTION Autoclave processing of carbon fiber prepregs is very common in the manufacture of composite structures for aerospace applications. There is however an inevitable build up of residual stresses within a composite part at the end of the autoclaving process. These stresses which are generated during the curing process are caused primarily due to the differential thermal expansion between the fibers and the matrix, and also due to resin volumetric shrinkage. Once fully cured and removed from the tool, the part tries to relieve the residual stresses by undergoing some deformation. This deformation, which is commonly referred to as Process Induced Deformation (PID), distorts the final shape or geometry of the structure. 1

2 A very common observation of the PID is the spring-in of angled sections such as a 'C' or an 'L' section, and warpage of a box or closed section structures. These distortions result in poor dimensional fidelity of composite parts, in that it causes problems in assembly because of poor fitup to mating structures [1]. This leads to manufacturing delays, and in many cases scrapping of parts, thereby increasing costs. A typical assembly mismatch is shown in figure 1. Fig. 1: Assembly mismatch due to part spring-in [1] For small sized components the PID are usually small enough that they can be ignored. But for larger components the PID can have a significant effect, and thus geometric compensation of the tool is usually required. Composite manufacturers usually have qualitative knowledge of the PID based on experience. A number of prototype parts are usually manufactured to determine the exact degree of tool compensation required [1]. However, this approach, which is essentially a trial and error approach, is feasible and cost effective only when the components are small and have low complexity. But for bigger and complex components, this approach would incur prohibitively huge costs and enormous development times. An alternative approach is employing a process modeling methodology to predict the final part shape for a particular tool geometry and processing condition (such as air temperature and pressure cycle). This approach would reduce the tool development cost by allowing the designer to evaluate and iterate the tool shape, using computer simulations before actually prototyping. This paper studies residual stresses induced in composite parts when cured and the adjoining PID using a computer modeling and simulation approach. Simple angled components such as L- and C-sections have been analyzed using a multiphysics composites processing model in ABAQUS/COMPRO Complete Component Architecture (CCA). The main PID that is studied here is the spring-in of the final parts. The results are then used to alter the tool geometry model accordingly and to check the final geometry of the composite part after tool compensation. 2.0 BACKGROUND Process-induced deformations (PID) of autoclaved parts result from stresses acting on, or generated within the part during processing. The stress that are exerted on the composite structure are due to the 2

3 autoclave pressure applied on the bag side and differential expansion of the tool and part on the tool side. Autoclave pressure also has an indirect effect, in that it increases the amount of stress transferred to the part from the tool side. This phenomenon is commonly known as tool-part interaction, and it usually generates a residual in-plane stress gradient through the thickness of the composite part. Further, during heating, the composite part and the tool expand at differently which is attributed to the coefficient of thermal expansion (CTE) mismatch between the tool and composite. The expanding tool stretches the plies closest to it due to friction. With resin cure, the plies that were stretched near tool are locked in the stretched position. This results in a non-uniform strain distribution in the through thickness direction of the composite and subsequently bending moments. Upon cooling and toolremoval, the part distorts due to the stress build-up. Residual stresses which are developed within the part are caused due to internal volume changes, primarily that of the resin. The main causes for this are the anisotropic thermal expansion and resin cure shrinkage, which cause micro- and macro-mechanical stress build-up in the corners of curved laminates resulting in spring-in. However the effect of micro-mechanical residual stresses is mostly seen in the strength of the material. They do not have much effect on the PID. It is predominantly the differential macro-mechanical stresses in the through thickness direction of the composite laminate that are the main cause of PID. If the structure is allowed to deform in order to relieve the residual stresses, it essentially becomes stress free on the macro-mechanical level [3]. The factors that affect PID are classified as intrinsic, which are material related, and extrinsic, which are process related. Intrinsic factors include anisotropic thermal expansion and resin cure shrinkage, while extrinsic factors include ply lay-up, part and tool geometry, cure cycle, tool material and tool surface. The intrinsic factors generate residual stresses at the material level (fiber-matrix level), and their effects cascade up through the length scales (part level). Extrinsic factors generate stresses at the part boundaries (at a part level) and their effect migrates down to the lowest length scale (fiber-matrix levels). The main effects of residual stress are reduction in strength and shape distortion. Stresses at the fiber-matrix, laminate, and structural levels affect the overall strength of the component, whereas stresses at the laminate and structural levels only affect the dimensional fidelity of the part [4]. 3.0 MODELING Composites process modeling usually employs an 'integrated sub-model' approach. This approach was first used by Loos and Springer (1983) to model composites processing. The concept behind this approach is to break down a very complex problem into a series of simpler problems, and solve each of them independently before integrating them to obtain the complete solution. Figure 2 shows the integrated sub-model approach as applied to the composites processing problem. The overall problem is tackled by dividing it into a series of sub-models viz. a 'thermochemical model' (for heat transfer and resin cure phenomena), a 'flow model' (for resin flow and compaction), and a 'stress model' (for residual stress and deformation analysis). 3

4 Fig. 2: Integrated Sub-model approach for composites process modeling (Spring, Loos 1983) [5] 4.0 RESULTS The complete process model is divided into a large number of small 'time-steps' for each of the submodels, and the modeled parameters are then updated at every step. Based on this approach, a composites process modeling program COMPRO was developed at University of British Columbia, Canada. COMPRO Complete Component Architecture CCA (COMPRO CCA) is basically a plug-in to 3rd part finite element based simulation software. It captures the complex and evolving properties of a composite material during the entire cure cycle. It simulates the impact of the evolving material properties on the thermal and cure history of the part, resin flow within a fully saturated part, and residual stress and part deformations of the part after tool removal. It consists of three analysis modules, viz. the Thermo-Chemical module, Flow-Compaction module, and Stress-Deformation module. In this paper however, the analyses have been performed using only the thermo-chemical and stressdeformation modules, i.e. the effects of flow-compaction have not been incorporated. The results obtained from the Thermo-chemical module are directly used in the analysis performed using the 4

5 Stress-Deformation module without taking into account the effects of flow-compaction. The final results therefore reflect only the effect of heat transfer and resin cure on the residual stresses generated in the composites and the associated PID. The prepreg material used in the analyses of the various components is the HEXCEL-AS It is a high performance composite ply which is used in the construction of primary aerospace structures. It has good impact resistance and damage tolerance for a wide range of applications. A dual-hold cure cycle is employed, based on the material data-sheet published by HEXCEL, with a peak hold temperature of 180 C, and a cure cycle duration of 400 min. The tool material is taken as Aluminum Thermo-Chemical Module The Thermo-Chemical module analyzes essentially the heat transfer from the surrounding air to or from the tool and composite part layup assembly. Further, the heat generated from within the part due the exothermic chemical reaction that takes place in the curing resin is also considered. This thermochemical analysis can be used to predict lag in the temperature between the air temperature and the part or tool temperature, temperature gradient within the part, as well as the temperature rise (due to the exothermic reaction) wherein the part temperature exceeds the surrounding air temperature. This analysis requires the orthotropic material properties for the composite part such as, resin thermal conductivity, specific heat capacity, resin heat of reaction etc. The material properties are updated at every solution step to account for the progression of cure and subsequent change in thermal properties. Following is the governing equation for the thermo-chemical analysis: Where: Here,, : Density of composite and resin : Specific heat capacity : Thermal conductivity : Resin heat generation : Resin degree of cure : Resin heat of reaction The expression is given by the Scholz equation [5] for cure kinetics as follows: 5

6 The values for the various terms in the above equation are given in Table 1. Table 1: Equation Parameter Values Parameter Value Initial fiber volume fraction Resin nominal density 1.3x10 3 kg/m 3 Resin Heat of Reaction 5.4x10 5 J/kg Activation energy 66.5 kj/gmole Pre-exponential cure rate coefficient 1.53x10 5 s -1 First exponential constant Second exponential constant Diffusion constant 43.1 Critical degree of cure at T=0 K Constant accounting for increase in critical resin degree of cure with temperature 5.475x10-3 K -1 To perform the analysis, convective heat transfer coefficients (HTC) are required for the boundary between the air and the tool or part. The HTC quantifies the rate of heat transfer between the surrounding fluid and the object surface temperature through the boundary layer. The value of HTC depends on the air velocity, pressure, temperature, surface orientation and geometry, and flow condition. 3.2 Stress-Deformation Module The Stress-Deformation module analyzes the residual stresses and strains in the composite part during the cure cycle. As described earlier, the residual stresses and PID are caused due to the difference in the thermo-mechanical properties of the resin and the fibers, volumetric shrinkage of the resin during cure, and tool-part interaction. In COMPRO the constitutive behavior of the resin is modeled as that of a fully viscoelastic material. The behavior of a viscoelastic material such as the resin is as shown with the help of a typical dual-hold cure cycle, figure 3. Before gelation, the resin is in a completely viscous state and does not carry any residual stresses. After gelation, the resin is in a rubbery' viscoelastic solid state with very short relaxation times. At the end of the final hold temperature, i.e. after the resin is fully cured, it behaves as a viscoelastic 'glassy' solid with very long relaxation times. It should be noted that the majority of the residual stresses are generated in the final cool-down phase of the cure cycle. 6

7 Fig.3: A typical dual-hold cure cycle showing resin behavior at different times The governing equation for a stress-deformation analysis is expressed as a function for the potential energy for a system: Where: : Internal work : Free/thermal strain tensor : Work done by external forces : Initial stress tensor : Strain tensor : Displacement vector : Stress tensor : Body forces : Material stiffness matrix : Surface forces 3.3 Modeling in ABAQUS The composite part and the processing tool were modeled in ABAQUS A discrete coordinate system was defined for the composite with the 1-direction along the 0 or reference ply orientation, and the 3-direction (normal) along the through thickness direction of the composite. For the thermochemical analysis, a 20 node solid brick element DC3D20 (heat transfer) was used for meshing the composite and tool parts. A temperature of 20 C was specified as the initial temperature for the tool and the part. 7

8 Composite HTC=80 W/m 2 K Tool HTC=20 W/m 2 K HTC=80 W/m 2 K HTC=20 W/m 2 K Fig. 4: Composite and tool assembly for L- and C-sections modeled in ABAQUS, showing heat transfer coefficients The HTC on the tool bottom side was taken as 20 W/m 2 K while that on the composite side was taken as 80 W/m 2 K. Both the tool and composite were modeled as solid homogeneous parts for the thermochemical analyses. Fig. 5: Air temperature cycle (cure cycle) A dual hold air temperature cycle with a maximum temperature of 180 C and a cure cycle duration of seconds was specified. A tie constraint, with the top surface of the tool as the master surface and the bottom surface of the composite as the slave surface, was assigned to the tool composite assembly. The results file obtained at the end of thermochemical analysis was used for the subsequent stress-deformation analysis. For the stress-deformation analysis, a 20 node brick element C3D20 (3D Stress) was used for meshing the composite and tool. The composite part was assigned an orthotropic material section, whereas 8

9 the tool was assigned a solid homogeneous material section. Symmetric plies were assigned to the composite part with an element relative thickness of 0.2. Two steps were defined in the analysis, one for the cure cycle, and the other for the tool-removal step. Fig. 6: Boundary conditions for the stress-deformation analysis Figure 6 shows the boundary conditions for the stress deformation analysis. As the assembly is symmetric about the vertical axis, only one half of the geometry was solved. The appropriate X, Y and Z-faces of the tool and composite were constrained for displacements along the respective axes. In addition, for the tool-removal step, the bottom edge of the composite was constrained along the Y- axis. A surface-surface contact with finite sliding, and with the top surface of the tool as the master surface, and the bottom surface of the composite as the slave surface, was defined in order to capture the tool-part interaction physics. A friction coefficient of 0.15 and limit shear stress of 40,000 N/m 2 was specified for the contact. The temperature field for the stress-deformation analysis was obtained from the results file of the thermochemical analysis performed earlier. For the analysis COMPRO uses material property values in the data file provided for the matrix, fiber and the composite material. 1.0 RESULTS AND DISCUSSION In this work, simulations were performed for an L-section (8 mm thick) with 40 [0,90] symmetric plies, and for a C-section (4 mm thick), with 20 [0,90] symmetric plies. The HEXCEL AS composite material was used. At the end of the thermochemical analysis, the degree of cure was checked, so as to ensure that the part was properly cured at the end of the cure cycle, and that the part was in thermal equilibrium. Figure 7 shows the composite cure with air temperature cycle. 9

10 Fig. 7: Composite cure with temperature cycle Next, at the end of the stress-deformation analysis, the stresses in the corner region of the parts were observed before and after tool-removal. After tool removal, the spring-in of the composite part was calculated from the angle which the deformed elements node made with the baseline (undeformed) element nodes. The total spring-in angle is calculated as the sum of the spring-in angle for each of the flanges of the part. The results were then compared with the spring-in of some published experimental results Fig. 8: Spring in for the L-Section (8mm thick, 40 plies, [0,90] S ) and L- section (4mm thick, 20 plies, [0,90] S ) (Scale factor=2) For the C-Section, four elements were selected along the thickness direction in the corner region where the maximum stresses were observed. The normal stresses of the plies in these elements were analyzed before and after tool-removal. Figure 9. shows the variation in the ply stresses along the thickness direction of the composite. 10

11 Fig. 9(a,b): Ply normal stresses for the C-Section, (a) Before tool-removal, (b) after tool-removal From figure 9a, it is observed that just before tool-removal, there is a large tensile stress at the bottom ply which is in contact with the tool. This could be attributed to the tool-part interaction that exists as a result of friction between the tool and the part. Also, it is observed that the composite part above the laminate symmetry line, especially the top ply is under compression. This could be attributed to the contraction of the part during the cool-down phase in the cure-cycle. As a result, there exists a huge variation in the nature of the stresses (tensile to compressive) from the bottom ply to the top ply. After tool removal, the part tries to relive the stresses by deforming. As a result, the tensile stresses at the bottom ply is relived by in plane contraction or shrinkage. On the other hand, the top ply, which is under compression, relives the stress by expanding along the plane. The net effect of this process, is the spring-in of the part, in that the flanges of the L- and C- sections deform inwards. Figure 8. shows the spring-in deformation of the L- and C-sections. The L-section undergoes a total spring-in of 0.68, while the C-section undergoes a spring-in of From this result, it can be inferred that thicker sections (8mm) deform less than relatively thinner sections (4mm). This can be attributed to the fact that thinner sections can relive residual stresses better than thicker sections, 11

12 as they are less stiff in the corner region. Further in this work, the effect of tool-compensation was studied for the L-Section. Here, the angle of the tool in the corner region was increased from 90 to 90.68, based on the spring-in angle obtained from the initial analysis, so that the composite part had a wider initial angle. A new analysis was then performed with the modified tool geometry, and the composite spring-in was then found to be Therefore the difference between the desired section surface and the actual surface is This is a significant change over the previous value of CONCLUSION Multiphysics simulation of the process-induced-deformations during autoclave processing of angled sections have been performed using ABAQUS/COMPRO CCA. It is found that tensile stresses in the bottom plies and the compressive stresses in the upper plies are generated as a result of the curing process. After tool-removal, the part springs-in so as to relieve these residual stresses. The tool geometry was compensated based on the initial values of the spring-in and the final part geometry matches quite closely with the desired shape. ACKNOWLEDGEMENT The authors gratefully acknowledge the partial support provided for this work by National Centre for Aerospace Innovation and Research, IIT-Bombay, a Department of Science and Technology- Government of India, The Boeing Company and IIT Bombay Collaboration. The authors also acknowledge Hindustan Aeronautics Limited and National Aerospace Laboratories for their technical support. REFERENCEx [1]Goran Fernlund and Anthony Floyd (2007), "Process Analysis and Tool Compensation for a Complex Composite Panel," 22nd Annual Technical Conference, Seattle.[2]Behrouz Tavakol (2007), "Prediction of Residual Stresses and Distortion of Carbon Fiber/Epoxy Composites Due to Curing Process," Wichita State University, Wichita, Master's Thesis.[3]G. Fernlund et al. 12

13 (2003), "Finite Element Based Prediction of Process-Induced Deformation of Autoclaved Composite Structures using 2D Analysis and 3D Structural Analysis," Composite Structures, vol. 62, pp [4]Goran Fernlund, Anoush Poursartip et al. (2003), "Residual Stress, Spring-in and Warpage in Autoclaved Parts," ICCM 14 Conference Proceedings, San Diego.[5]Andrew Johnston (1997), "An Integrated Model of the Development of Process-Induced Deformation in Autoclave Processing of Composite Strucutres," University of British Columbia, Vancouver, PhD. Thesis.[6]Carolyne Albert and Goran Fernlund (2002), "Spring-in and Warpage of Angled Composite Laminates," Composites Science and Technology, vol. 62, pp x 13