In this section, the proposed model is tested by means of a well known three-dimensional example with clear matrix crushing and matrix cracking damage developments. This test consists of a low velocity impact -7.08ms-1- on a laminate [0/90] a formed by 21 alternate laminae, see Figure 4, made of carbon fibres and epoxy resin. The composite obtained is a transversally isotropic fibre reinforced composite material with a volume fraction of 60%. Experimental tests were conducted by Hallet (1997) using a Hopkinson bar apparatus, see (Hou et al., 2000) for more details of the set-up of this experiment. Basically, the projectile is a titanium alloy rod with a diameter of 9.55 mm and a total length of 500 mm and its head is rounded in order to damp the vibrations. The mass of the projectile was calibrated to 260 g to strictly replicate the experiment.
The dimensions of the laminate were 2.6x85x85 mm3 and it is supported by a steel ring with an inner diameter of 45 mm. In the experiments performed by Hallet (1997), the impact velocity was measured by infra-red timing gates just before the laminate was struck. C-scan and dye contrasts were used to detect damage after impact. The results of dye contrast test showed that the projectile impacted with an initial velocity of 7.08 ms-1 and, hence, this is the impact velocity that has been used in these numerical tests. In the experiments by Hallet (1997) as
well as in the numerical tests conducted by Hou et al. (2000), a matrix crushing zone was observed just beneath the contact region, i. e. in the through-thickness compression region under the projectile. The numerical result for matrix crushing region from the proposed model is depicted in Figure 5. It may be observed that the matrix crushing zones are located in agreement with the experimental results by Hallet (1997); Hou et al. (2000). The progressive development of those regions is more realistic than the result obtained using just stress failure criteria as depicted in Figure (6) which provides Boolean values for the damage variables without considering any progression of the damage. In the computational results using PDM, neither fibre rupture nor fibre kinking were developed as expected with that impact velocity. To turn off the damage modes according to physical reality is an excellent characteristic of PDM.
This chapter has provided an overview of the different techniques used for modelling damage in composites briefly showing the current state-of-art of the topic. Basically, from a computational point of view, there are two main trends:
• failure criteria which generally use a stress quadratic form.
• a progressive evolution of the damage.
The authorts choice is the second one for two main reasons. Firstly, because failure criteria is creating Boolean values for deciding when a finite element is deleted or split which, in turn, cause numerical instabilities and, eventually, divergence in explicit finite element simulations. Secondly, the progression of damage, even if it is sudden, evolves sequentially in a microscopic scale which reasonably makes the progressive damage models more realistic. Following this second tendency, the author has presented a progressive damage model (PDM) for fibre reinforced composites. The approach is based in a directional computation and a progressive growth of of damage modes depending upon the stress state and strain rate amongst other variables. Moreover, the constitutive law is implicitly relying upon the strain rate, which makes the model suitable for a wide range of strain rate values including impact. The computation is, in general, intended for time stepping numerical methods and, in particular, for the explicit FEM. The PDM algorithm is offered for straightforward
Finite Element Analysis of Progressive
Degradation versus Failure Stress Criteria on Composite Damage Mechanics
implementation in an explicit FEM code either commercial software package or in-house code. The outcome obtained by using PDM for tension and compression tests provide the expected progression of the damage variables, being able to determine the corresponding damage modes associated with each stress state and rate of strain, eventually leading to the expected behaviour. Furthermore, the computational results by using PDM for the low velocity impact on a laminate were in an excellent agreement with the experimental observations of matrix cracking and matrix crushing which, eventually, caused the delamination in those damaged regions of the laminate.
Composite Materials – Ecodesign and Analysis
Fig. 6. Matrix cracking pattern using a classical failure criterium based on stress components. The elements in red fulfilled the criterium which means that they are not withstanding loads any longer.
Fig. 7. Sequential matrix cracking pattern observed during simulation by explicit FEM using PDM. A time progressive evolution of this damage mode, which eventually turned into delamination, is observed in an excellent agreement with the experimental observations.
Bonded Composite Patch Repairs on Cracked Aluminum Plates: Theory, Modeling and Experiments
Fabrizio Ricci, Francesco Franco and Nicola Montefusco
University of Naples "Federico II", Department of Aerospace Engineering
Composite patches, bonded on cracked or corroded metallic aircraft structures, have shown to be a highly cost effective method for extending the service life and maintaining high structural efficiency (Baker & Jones, 1988; Baker, 1993; Molent et al., 1989; Baker et al., 1984; Torkington, 1991; Bartholomeus, 1991).
Damage tolerant and fail-safe design of aircraft, aerospace and civil structures requires a substantial amount of inspection and defects-monitoring at regular intervals. There is a large number of high-cost inventory of aircraft structures in operation throughout Europe and the world, that are undergoing continuous degradation through aging. Moreover, this number is increasing by around 5% every year, resulting in significant negative impact on the economy of many nations. The degradation of defects critical structures is controlled through careful and expensive regularly scheduled inspections in an effort to reduce their risk of failure.
The replacement of a damaged structural component has a relevant impact on the life cycle cost of an airplane. Bonded composite patches for repairing cracks and defects in aircraft structures have been widely used in the last years. This technology offers many advantages over mechanical fastening or riveting, including improved fatigue behavior, restored stiffness and strength, reduced corrosion and readily formed into complex shapes. The repair of metal structures with composite materials is a technology that was first introduced in Australia in the early 1970s and later in USA in early 1980s. It is now estimated that over 10 000 flying patch repairs, for corrosion and fatigue damages, have been performed on Australian and US military aircraft (Christian et al., 1992; Umamaheswar & Singh, 1999; Roach, 1995). This technology was first used for the repair of military aircraft and then applied also to civil aircraft. The success of a bonding repair depends on the properties of both the adhesive and the patch. The quality of the repair depends upon bonding process and surface treatment as well. Carbon-epoxy composites have been mostly used in aeronautics due to their high stiffness and strength to weight ratios. The performance of the adhesive plays a key role in the successful utilization of bonded composite patch repairs.
The role of a bonded composite patch is to restore the stress state modified by the presence of the crack. The stress intensity factor is then reduced by the presence of the patch. Many authors have already investigated the behavior of metallic structures repaired by composite
patches. Baker and Jones (Baker & Jones, 1988) studied an aluminum panel repaired with composite patches. For a repaired cracked plate they showed that the stress intensity factor does not increase indefinitely with the crack length, as it asymptotically reaches a limit value. According to Baker’s results, Rose (Rose, 1981 and 1982) showed that the stress intensity factor range of a repaired structure does not depend on the crack length if the crack grows up below the repair. As a result, the crack growth rate does not depend on of crack length according to the Paris law. Klug (Klug et al., 1999) investigated the fatigue behaviour of pre-cracked 2024-T3 aluminum plates repaired with a bonded carbon/ epoxy patch. Single sided repairs were found to provide about a 4-5 times improvement in the fatigue life.
After these early works many authors have addressed many numerical and experimental aspects. Naboulsi, Schubbe and Mall (Nabulosi & Mall, 1996; Schubbe & Mall, 1999) have analyzed the modeling of the composite and adhesive layers, using the three layer technique in comparison with the high computational cost of the three dimensional Finite Element models. Naboulsi and Mall (Nabulosi & Mall, 1998) have successively adopted the three layer technique for the nonlinear analysis of the repaired structure in order to take in account large displacements and material nonlinearities. Chung and Yang (Chung & Yang, 2002) and Jones, Whittingham and Marshall (Jones et al., 2002) have investigated the fracture and the crack growth behavior in a more complex structure, such as stiffened panel, deriving some design formulas. Tong and Sun (Tong and Sun, 2003) have presented a novel finite element formulation for developing adhesive elements and conducting a simplified nonlinear stress analysis of bonded repairs in curved structures. Some other authors have focused their attention on the optimal design of the bonded patches, by finite element models, in terms of edge taper (Wang et al., 2005) and in-plane shape (Mahadesh & Hakeem, 2000).
Some of the above mentioned numerical activities have been compared with experimental data measured with reference to the stress intensity factor and fatigue life of the repaired structural elements (Schubbe & Mall, 1999; Wang et al., 2005;).
The aim of this work is to review the capability of finite element models in estimating the mechanical behavior of metallic panels repaired by composite patches. The attention has been focused on those commercial codes implementing the "quarter-point location" formulation. The interest in commercial finite element codes is due to their use in most of the industrial applications. Furthermore the validation of the finite element procedures for a metallic panel with a composite patch repair is a promising result for the analysis of composite structures to be repaired with composite patches.
The numerical analyses, limited to the case of mode I (opening crack), have been strongly supported by well known theoretical formulations and several experimental tests. Moreover, the experimental data allowed a comparison among different patches, adhesives and surface preparation properties.
In this work a repair with a single patch – single sided configuration – (i. e. bonded only on one side of the panel) has been considered. This configuration could avoid the removal of the damaged component and in general could lead to a significant reduction of time and costs of repair operations.
Section 2 of the paper presents the geometry of the panel used as test-case. Section 3 reviews the mechanical behavior of the cracked panel. The mechanical behavior of the repaired panel, estimated by the numerical models, is presented in Section 4 and the comparison with the experimental data is discussed in Section 5. Finally, Section 6 summarizes the work conclusions and outlines some final considerations.