Development of a Numerical Tool for Laminate Composite Distortion Computation Through a Dual-Approach Strategy +
Footnote †: This paper is an extended version of “Shape distortion prediction of high temperature curing laminates through a transient multi-physics numerical model” paper published in the international conference: AIAA SCITECH 2024 Forum, Orlando, FL, USA, 8-12 January 2024.  
in a single step [1; 2; 3]. Generally, the aerospace industry requires high tolerance accuracy for parts and assemblies, which creates real engineering challenges, especially for moving parts like control surfaces--for instance, the Bell Agusta BA609 inboard flaperon is an aerodynamic control element with several complex and critical features [4].  
The investigation of global distortion starts with identifying the mechanisms that generate residual stress [5]. Developing computational models requires deep knowledge of the mechanisms generating the geometrical variations. We can look at residual stress depending on its origin and thermoelastic or non-thermoelastic nature. We will deal with micro-scale and macro-scale residual stress for a cured part. Micro-scale residual stress will develop between the fibers and the polymeric matrix and is caused by (a) CTE mismatch of fibers and resin, (b) resin shrinkage in the curing process, and (c) moisture absorption. The micro-scale residual stress does not cause part distortion.  
The source of significant geometry changes is the macro-scale residual stress. The individual ply behavior is anisotropic; the tooling and the individual plies influence the macro-scale residual stress. A general but entirely accurate assumption for thermoelastic residual stress is that the full-scale phenomena can be interpreted as a difference between in-plane thermal strain and orthogonal (through laminate thickness) thermal strain. On the other hand, non-thermoelastic stress develops through several distinct mechanisms. It leads to non-reversible geometry distortion: tool-part interaction [6], chemical shrinkage during polymerization [7], consolidation [8], laminate through-thickness degree of cure [9], and fiber volume fraction gradients [10]. An overview of these mechanisms and a high-level approach to developing a numerical tool for evaluating composite distortion is described in Figure 1.  
Multiple concurring factors cause residual stresses and the resulting distortion. Out-of-plane deformations of curved parts are caused by resin cure shrinkage and thermal anisotropy as through-thickness contraction occurs. Both factors influence distortion in different phases of the manufacturing process: shrinkage occurs during curing, and anisotropy influences cooling [11; 12].  
Tool-part interaction is an essential factor that influences distortion. The residual stress between a tool and a part is, in essence, caused by the different thermal behavior of the two elements, leading to shearing stress between them. The stress at the tool face is transmitted through the thickness to a certain point due to the slipping motion between the plies and the shear compliance of the resin [12; 13]. For flat parts, such through-thickness stress gradients lead to warpage when the part and tool are separated [14]. The intrinsic nature and specificity of laminate manufacturing factors like through-thickness fiber volume fraction gradient and fiber alignment deviations (ply misalignment, fibers wrinkling, etc.) will lead to residual stresses and distortion [15].  
Figure 1: Illustration of distortion mechanisms in laminates.  
Although environmental factors, such as moisture absorption, can cause distortion [16], the current study will only focus on distortions induced by thermal changes and phase changes in polymer matrices.