An isogeometric continuum shell element for non-linear analysis

A geometrically nonlinear variable-kinematics continuum shell element for the analyses of laminated composites

This paper presents detailed experimental information on mode-II delamination development in fibre/epoxy composite materials and provides observations about the process zone in the vicinity of the crack tip. It is shown that the energy dissipated in delamination propagation is spent on two ways (i) creating new fracture surfaces (delamination) and (ii) nonlinear shear deformation in the composite plies adjacent to the delaminating interface. Therefore, the nonlinear process zone is not restricted to the resin-rich interface between the layers, but also extends into the fibre/epoxy composite layers. This is different from the conventional assumption in modelling delamination using cohesive elements where the fibre/epoxy layers are fully linear-elastic and the process zone is lumped at the plane of fracture. Based on the accurately measured displacement field around the crack tip, the experimental traction-separation relation at the interface is found to be trapezoidal which is again different from the conventional bilinear cohesive law.

Carbon fiber epoxy laminates are extensively used in the aerospace industry as they offer a combination of high performance with relatively low weight. However, damage may occur in these materials, either at the manufacturing level or during use, which may affect their structural integrity. Among the type of damage which may occur, delamination is a common defect which causes a reduction in compressive strength and thus limits the life of laminated composites. If undetected, delamination may propagate during use due to mechanical loads and in the worst case may cause fracture of the material. Therefore, delamination in composite materials needs to be efficiently detected and accurately quantified for safety and economic reasons. Because of their heterogeneity, multi-layered structure and anisotropy, the inspection of composite materials remains difficult with conventional NDT methods. A method making use of Foucault currents, and relying on the principle of electromagnetic induction, can be adapted for the detection and characterization of damage in composite materials. The use of Foucault currents in characterizing delaminated areas at interfaces between plies in carbon fiber/epoxy laminates is addressed in this paper. It is demonstrated that Foucault currents can accurately detect and quantify delamination in CFRP materials. Furthermore, the potential of this technique for monitoring defect propagation in composite materials is discussed.

The perennial challenge for the industry is to make parts, assemblies and machinery lighter and more efficient. This has led to progressively wider application of composites due to their excellent strength, stiffness and corrosion resistance properties. Composite components are assembled predominantly by fastening, which makes drilling a common machining process for such components. Delamination of the component surface at entry and exit of the drill is a drilling defect frequently encountered. Assessment of the severity of the delamination is necessary for correction and improvement of the performance of the parts and assemblies. Over a period of time, several factors have been suggested as the index of delamination for comparison and control. Also, various techniques are being adopted to measure the extent and severity of delamination so as to calculate the assessment factor. This study aims to present and review the different means and methods for the assessment of delamination.

Among the failure modes of composite materials, delamination is the most striking one. It may result in the reduction of stiffness and long-term performance of composite materials. The initiation stage is very crucial in delamination. This is because initiation stage requires higher amount of force, and after this stage, there is a stable propagation of delamination that requires little force and causes the failure of the structure. Initiation of delamination consists of two main stages including minor initiation and major initiation. These two stages are vital stages in the delamination process. Understanding the delamination behavior and their internal micro events in these stages may lead to better design and result in enhanced strength against crack initiation. This article proposes a combined method to discriminate various fracture mechanisms in the initiation of delamination. The combination of sentry function analysis and frequency analysis of acoustic emission (AE) waveforms are used to analyze crack initiation and to discriminate its internal micro failures during mode I delamination. Discrimination process is derived from the power spectrum density of AE waveform in distinct frequency intervals. Scanning electron microscopy (SEM) observation was used to determine different fracture mechanisms and associate these observed fracture mechanisms and their equivalent AE signal frequency range. It is shown that this combined method is a powerful device to study the behavior of the initiation of delamination.

Chapter 2 - Strategies for dynamic failure analysis on aerospace structures

A half-analytical elastic solution for 2D analysis of cracked pavements

Interface Fracture and Delaminations in Composite Materials

This paper presents a fast engineering tool for the analysis of the mechanical fields in cracked pavements. The pavement structure is reduced to three elastic and homogeneous equivalent layers resting on a soil. The soil is modelled by one layer, named shear layer, connected to Winkler's springs in order to ensure the transfer of shear stresses between the pavement structure and the springs. The whole four-layer system (3 pavement layers connected to the shear layer) is modelled using a simplified model (M4-5n) developed for the analysis of delamination in composite materials. For the case of 2D plane strain, a system of twelve equations is written analytically. These second order differential equations are solved by the finite difference method (Newmark). In the case of a pavement containing a vertical cracking through one layer, the half-analytical solutions are obtained in less than one second CPU. This tool, called M4-5nW, thus allows parametrical studies such as the distribution of mechanical fields (especially interface stresses) as function of the load position more or less distant from the vertical crack. This new modelling shows its effectiveness compared to the use of a conventional finite element code.

Failure mode and strength of uni-directional composite single lap bonded joints with different bonding methods

Low frequency NDT techniques for the detection of disbonds and delaminations: British journal of nondestructive testing, vol. 32, no. 9, pp. 454–461 (Sep. 1990)

Abstract: A fracture energy approach for modelling mixed‐mode delamination of composite materials and other bonded structures is introduced. The model is incorporated within an explicit finite element (FE) code and ties layered shell elements together via a stiffness condition, a failure criterion and post‐failure damage law. The procedure for predictive modelling of delamination using the approach is described and the set of required input parameters is presented. A benchmark test comparing experimental results for a continuous filament random E‐glass/polyester composite and explicit FE simulations for standard fracture toughness tests for a range of mode mixities is included.

This work is focused on the development of instrumental radiographic methods for detection of delaminations in layered carbon fibre reinforced plastic composites used in the aerospace industry. The main limitation of current visualisation techniques is a very limited possibility to image so-called closed delaminations in which delaminated layers are in contact practically with no physical gap. In this contribution we report the development of innovative methods for closed delamination detection using an X-ray phase contrast technique for which the distance between delamination surfaces is not relevant. The approach is based on the energetic sensitivity of phase-enhanced radiography. Based on the applied methodology, we can distinguish both closed and open delamination. Further we have demonstrated the possibility to visualise open delaminations characterised by a physical gap between delaminated layers. This delamination type was successfully identified and visualized utilizing a high resolution and computed tomography table-top technique based on proper beam-hardening effect correction.

A generalization of a NURBS based parametric mesh-free method (NPMM), recently proposed by Shaw and Roy (2008), is considered. A key feature of this parametric formulation is a geometric map that provides a local bijection between the physical domain and a rectangular parametric domain. This enables constructions of shape functions and their derivatives over the parametric domain whilst satisfying polynomial reproduction and interpolation properties over the (non-rectangular) physical domain. Hence the NPMM enables higher-dimensional B-spline based functional approximations over non-rectangular domains even as the NURBS basis functions are constructed via the usual tensor products of their one-dimensional counterparts. Nevertheless the method still lacks the universality that the FEM enjoys. In particular, for many non-simply connected domains, the geometric map may not be locally bijective everywhere and this severely restricts the general applicability of the NPMM. In this paper, a piecewise form of the NPMM is proposed, wherein the domain is decomposed into a collection of simply connected sub-domains or element patches (analogous to the FEM). The NPMM is then employed over each sub-domain without affecting the continuity of approximated functions across inter-sub-domain boundaries. This is quite unlike the usual FEM. The proposed procedure not only possesses the generality of the FEM, it is also equipped with higher order, globally smooth and interpolating basis functions. It may thus be interpreted as a seamless bridge between the FEM and mesh-free methods. In the context of weak implementations of the piecewise NPMM, we propose a conformal knot-grid integration scheme. Finally, we illustrate these schemes for weak numerical solutions of a few linear and nonlinear boundary value problems of engineering interest.

This study presents a comprehensive finite element analysis to compare the performance of different element formulations (classic shell elements, solid elements, and continuum shell elements) in simulating the hot-forming process at 725 °C of a complex Ti-6Al-4V aerospace component with an initial blank thickness of 1.6 mm (0.063 inches). The Ti-6Al-4V blank is modeled as a deformable body exhibiting anisotropic plastic behavior, whereas the forming tools (matrix and punch) are assumed to be rigid bodies. The simulation accounts for temperature and strain rate effects on the material properties, incorporating phenomena such as friction and anisotropy. Three different element types are studied and compared: S4R and S4 (classic shells), C3D8R and C3D8 (solids), and SC8R (continuum shell with reduced integration). Finally, the model is validated by comparing the predicted final part geometry, especially the thickness distribution, against the experimental measurements. The model can also predict the springback effect on the final geometry. The SC8R continuum shell element provides the smoothest representation of thickness variations along critical regions of the final part. The study highlights the importance of selecting the appropriate element type for the accurate simulation of hot-forming processes involving large deformations and complex contact conditions. The ability of continuum shell elements to accurately capture the thickness variations makes them an ideal candidate for such applications.