Chapter 4. Numerical simulations and experimental experiences of impact on ... technology solutions, it is necessary to use the ability of powerful computational ... from the first time that an airplane has disconnected the wheels off the ground .... Traditional finite element approach cannot capture details of all individual failure.
Chapter 4 Numerical simulations and experimental experiences of impact on composite structures. Marulo F., Guida M., Maio L., Ricci F. - University of Naples "Federico II", Italy ABSTRACT
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KEYWORDS
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INTRODUCTION
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1. COMPUTATIONAL DAMAGE MECHANICS FOR COMPOSITE 1.1. DAMAGE PROGRESSION 1.1.1. Challenging issue in designing composites 1.1.2. Material models 1.1.3. The continuum damage mechanics: a damage constitutive model 1.1.4. The constitutive response 2. MATERIAL TESTING AND COMPONENT VALIDATION 2.1. MATERIAL CALIBRATION 2.2. MICROMECHANICAL CALIBRATION: FE MODELLING 2.2.1. Tensile test 2.2.2. Compression, tensile open hole and compression open hole results 2.2.3. Simulation of Low Energy Impact 2.2.4. Cohesive input properties 2.2.5. Mesh size 2.2.6. Cohesive stiffness 2.2.7. Energies at damage onset 2.2.8. Calibration of the cohesive properties 2.2.9. Numerical simulation
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CONCLUSIONS AND FUTURE TRENDS
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Abstract The composite material and the qualification/certification of composite structures require rigorous analysis validated by the experiments, due to the sensitivity of composites to out-of-plane loads, the multiplicity of composite failure modes and the lack of standard analytical methods. Because of the need to compare measured properties and performance on a common basis, users and producers of materials use standardized test methods such as those developed by the American Society for Testing and Materials (ASTM) and the International Organization for Standardization (ISO). These standards prescribe the method by which the test specimen will be prepared and tested, as well as how the test results will be analysed and reported. The chapter contains information about mechanical tests and numerical simulations in general as well as tension, compression, shear, and impact tests in particular, then the composite application about the aerospace structure and the evaluation of the dynamic response of the composite materials.
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keywords Material testing, damage mechanics for composite, low impact, FE modelling, aerospace structure
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Introduction This chapter deals with the composite material and their application in the aeronautical field. Considering that the aerospace industry has a strong certification and compliance requirement, with consequences on development cost and technology solutions, it is necessary to use the ability of powerful computational methods to resolve material behaviour at different scales and communicate across them is fostering unprecedented advances in multi-scale modelling. These models provide in-depth understanding of material deformation and failure that can revolutionize integrated structure-material design, and an added value is represented by the experimental tests on small-scale models. The widespread use of composite materials in aeronautical, and aerospace industry in general, is not only the challenge of our times. The use of composites is born from the first time that an airplane has disconnected the wheels off the ground. The development of composite materials was accelerated by the outbreak of World War II, since 1940 the fuselage of the Spitfire was designed and built by the company Aero Research Ltd in Duxford, in material made from flax fibers not twisted dipped in phenolic resin and was developed by Norman de Bruyne and Malcolm Gordon, [1]. Nowadays the news is not what the big aeronautical manufacturers use the composite but how much composite materials they have used. The novelty is that the Boeing company make flying the 787 Dreamliner aircraft where 50% of structure is made up of composite. Airbus with the flight of the A350XWB airplane now boast a 53% usage of composite material among its long products. A composite is a macroscopic (visible to the naked eye) combination of two or more materials which results in a material possessing structural properties none of the constituent materials possess individually. Because the materials are not soluble in one another, they retain their identity. The composites have amply demonstrated their functionality in increasingly diverse fields. The recent development and the development of new technologies have
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allowed to composites to compete with metals, even more, in the aeronautical field the composite materials are widely used especially thanks to the saving in weight combined high fatigue and corrosion resistance. More parts of an aircraft use composite materials: parts of wings and tails, fuselages, antennas, landing gear, floors seats, interior panels, tanks, helicopter blades. Not only the light weight aspect is a peculiarity of the composite materials, but the strength is often a defining feature, as well as high-temperature resistant composite materials allow to reduce fuel consumption, improve efficiency and reduce direct operating costs of aircrafts. The most important characteristic of the composite materials is that they can be layered, with the fibres in each layer running in a different direction. This allows an engineer to design structures with unique properties, furthermore a structure can be designed so that it will bend in one direction, but not another. The aeronautical structures certification requirements are basically the same regardless of the material used to produce them. The certification of composite component is more complex than that of metal elements (aluminium alloys, titanium and steels); this difficulty is due to the wide variability of the properties of composites and not to the current total mastery of design technique with these materials. The composites are produced from perishable raw materials, such as polymeric resins; for this reason, they require a greater quality control. The attitude of authorities towards these materials is as follows: the structures made of composite should not submit the risks to aircraft operators are higher than those that accept to giving themselves to metallic materials. It is the responsibility of the designer to ensure these security levels. In 1978 the Federal Aviation Administration (FAA) Advisory Circular AC20-107 issued the certification of aeronautical structures made of composite materials, [2]. It is a short document in which it is specified that the composite design must reach a level of security at least equivalent to that required by the metal structures. Analysis, whether performed by closed form solutions or finite element models, can be useful in design and certification of impact-damaged composite structures. The
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state of the art is such that analysis cannot stand by itself but can be useful in directing and analysing test results and expanding test data to untested configurations by semiempirical methods. Impact damage is one of the main problems that composite structures face, hence, there needs to be a way of reducing that damage when it occurs, reducing it enough so that the integrity of the structure is not compromised. There are a number of solutions to improve impact resistance and damage of composite materials, such as fiber toughening, matrix toughening, interface toughening, through-the-thickness reinforcements, and selective interlayers and hybrids. One of the possible to reduce impact damage in composite structures is to embed the shape memory alloy (SMA) wires inside the polymer composites due to their superelastic behaviour allowing remarkably high strain to-failure and recoverable strain and their capability to generate recovery tensile stresses and hence reduce the deflections and the inplane strains and stresses of the structure, [3]. Then, honeycomb material offers a great possibility to optimize the energy distribution during the impact, for example the cores made from continuous fibre reinforced composites shows better response to impact loading compared to that of short fibre reinforced, exhibiting a large elastic region and higher peak loads, [4]. Also the importance of the fruition of FML development marks a step in the long history of research starting in 1945 at Fokker, where earlier bonding experience at de Havilland inspired investigation into the improved properties of bonded aluminium laminates compared to monolithic aluminium. Later, NASA got interested in reinforcing metal parts with composite materials as part of the Space Shuttle program led to the introduction of fibers to the bond layers, and the concept of FMLs was born. Although GLARE is a composite material, its material properties and fabrication are very similar to bulk aluminium metal sheets, [5]. It has far less in common with composite structures when it comes to design, manufacture, inspection or maintenance. GLARE parts are constructed and repaired using mostly conventional metal material techniques.
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1. Computational Damage Mechanics for Composite 1.1.
Damage progression
1.1.1. Challenging issue in designing composites A challenging issue in designing composites is the prediction of various failure modes, such as fiber breakage, matrix cracking, fiber/matrix debonding, fiber kinking, and delamination between adjacent plies, [7]. The difficulty of the problem was evidenced by the World Wide Failure Exercise, an international activity launched by Hinton, Kaddour and Soden, [8] to establish the status of currently available theoretical methods for predicting material failure in fiber reinforced polymer composites materials in the course of which 12 of the leading theories for predicting failure in composite laminates have been tested against experimental evidence. This event revealed that very few theories successfully predicted failure of composite coupons deformed quasi statically. In general, the load carrying capacity of a structure does not vanish as soon as either failure or damage ensues at a material point and the structure can support additional load before it eventually fails. Thus it is important to quantify damage caused by the initiation of a failure mode and study its development and progression and the eventual failure of a structure with an increase in the applied load. Therefore, in many structural applications, the progressive failure analysis is required to predict composite structure mechanical response under various loading conditions. Failure and damage in laminated structures can be studied by using a micro-mechanics approach [42] (see Ref. [7] for more information) but the damage studied at the constituent level is only computationally expensive for a real size problem. The alternative is an approach based on continuum damage mechanics (CDM), [43], in which material properties of the composite have been homogenized and both damage and failure are studied at the ply/lamina level; e.g., see reference [43] - [47]. However, a micromechanical approach can be used to deduce effective properties of a ply and CDM approach to study failure and damage at the lamina level, ref. [42].
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1.1.2. Material models The inhomogeneous and not-isotropic nature of composite materials result in fracture and failure behaviours unlike that of conventional metallic alloys. As seen before, the damage can initiate and propagate in many ways: many different mechanisms can occur (interfacial debonding, fiber microbuckling, matrix cracking, fiber breakage, delamination, etc.) and damage growth is not self-similar. In multidirectional composite laminates, damage accumulates during the loading process and the final failure occurs as a result of damage accumulation and stress re-distribution. The ultimate failure load is higher than the damage onset load. Therefore, it is useful to have models capable to predict the onset of material degradation, the effect of the non-critical damage mechanisms on the stiffness of the laminate and ultimate structural failure. Traditional finite element approach cannot capture details of all individual failure modes, but needs to make further approximations; therefore, the key is to know how to make the right approximations. Material failure is treated simply and suitably on mesoscale and macroscale, but in this way it’s not possible account for detailed differences between failure mechanisms neither it’s possible to consider other phenomena on microscale. Today, typically, numerical models based on lamina-level failure criteria are used to simulate the damage of the fiber-reinforced composite material, although with well-accepted limitations. In these constitutive models, composites are modelled as orthotropic linear elastic materials within the failure surface; the failure surface is defined by the failure criterion (damage onset criterion) as maximum stress/strain criterion, Hashin's criterion, Christensen's criterion, Chang-Chang’s criterion, Puck's criterion, LARC etc.; they are based on stress or strain components; beyond the failure surface, elastic properties are degraded according to laws defined by the material model. The degradation schemes used to reduce the material properties once failure initiated are two: a) ply properties are reduced to a value close to zero in the finite element that satisfied the criterion of damage; b) damage parameters are used to degrade ply properties in a continuous form (Continuum Damage Mechanics) in the finite elements that satisfied the damage onset condition. 8
Figure 1 – Non-progressive degradation of the elastic properties.
The first scheme uses a ply discount method to degrade the elastic properties of the ply from its undamaged state to a fully damaged state; in the specific, the scalar components of the stiffness tensor are reduced to approximately zero when damage is predicted (null stiffness can lead to numerical instability). Elastic properties are dependent on field variables. After a failure index has exceeded 1.0, the corresponding user-defined field variable is made to transit from 0 (undamaged) to 1 (fully damaged) instantaneously and it continues to have the value 1.0 even though the stresses may reduce significantly, which ensures that the material does not “heal” after it has become damaged. The material models based on this scheme are easy to use and require few input parameters. However, they cannot represent with satisfactory accuracy the progressive reduction of the stiffness of a laminate as a result of the accumulation of damage modes. Tensile fiber mode: 2
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æs ö æ s xy ö e = ç xx ÷ + b ç ÷ -1 s xx > 0 è Xt ø è Sc ø e2 ³ 0: damaged, 𝐸 = 𝐸 = 𝐺 = 𝜈 = 𝜈 à 0; se e2ft < 0: elastic behavior. Se ft x y xy yx xy 2 ft
Compressive fiber mode:
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æs ö e = ç xx ÷ - 1 s xx < 0 è Xc ø 2 e ³ 0: damaged, 𝐸 = 𝜈 = 𝜈 = à; se e2fc < 0: elastic behavior. Se fc x yx xy 2 fc
Tensile matrix mode: 2
s yy
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æ s yy ö æ s xy ö e =ç ÷ +ç ÷ -1 >0 è Yt ø è Sc ø 2 mt
2 2 Se emt ³ 0: damaged, 𝐸y = 𝜈yx = 0 ⇒ 𝐺xy à 0; se emt < 0: elastic behaviour.
Compressive matrix mode: 2 2 ù æ s yy ö æ s xy ö 2 æ s yy ö éæ Yc ö e =ç ÷ + êç ÷ - 1ú ç ÷+ç ÷ -1 úû è Yc ø è Sc ø è 2Sc ø êëè 2Sc ø s yy < 0 2 mc
2 2 Se emc ³ 0 : damaged, 𝐸y = 𝜈yx = 𝜈xy à 0 ⇒ 𝐺xy à 0; se emc < 0 : elastic behavior.
e ft , e fc, emt , emc are failure indices of the considered damage modes.
“x” is the fiber direction; “y” is transverse. Xc is the longitudinal compressive strength (absolute value is used). Xt is the longitudinal tensile strength (absolute value is used). Yc is the transverse compressive strength, b-axis (positive value), see below. Yt is the transverse tensile strength. Sc is the shear strength. β is a weighting factor for shear term in tensile fiber mode. table 1 – Chang/Chang (material model MAT_54 in LSDYNA) damage onset criteria. The stresses are compared to the measured strength values by applying different relations depending on the damage mode. After a layer has experienced matrix failure, for e.g., the material properties Ey and Gxy of the damaged layer are multiplied by a factor according to the degradation rules, ref. [28] and [40].
Failure modes in laminated composites are strongly dependent on geometry, loading direction, and ply orientation. One distinguishes for convenience in-plane failure modes and transverse failure modes (associated with interlaminar shear or peel stress). However, when the composite is loaded in-plane, only in-plane failure modes need to be considered, which can be done for each ply individually. For a unidirectional ply, at least four failure modes can be considered: matrix tensile cracking, matrix compression, fiber breakage and fiber buckling. All the mechanisms, with the exception of fiber breakage, can cause compression failure in laminated composites.
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Figure 2 – A schematic presentation of different degradation rules. The simple rule uses knockdown factors close to zero; the constant stress model assumes that the damaged element will carry its failure load but no additional loads; in real case the ply behaviour is something between these two models, therefore, models that use gradual unloading have been developed.
The issue of damage growth in fiber reinforced plastic (FRP) laminated composites has been addressed by an ever-increasing number of researchers through the use of Continuum Damage Mechanics (CDM). Usually it is recognized that CDM started with the papers by Kachanov (1958) and Rabotnov (1968). However, the use of CDM for the simulation of composite behaviours has been popularized in the 1990s by Ladeveze, [7] and Talreja [10]. The Continuum Damage Mechanics approach focuses on the effect of the presence of micro-failures in the material. In detail, it attempts to predict the effect of microscale defects and damage at a macroscale by making assumptions about the nature of the damage and its effect on the macroscale properties (e.g. elastic moduli) of the material. This damage theory describes the damage, i.e. the appearance of cracks, as a state variable that can be expressed as a scalar or as a tensor to quantify the isotropic or anisotropic damage. Therefore, the CDM theories capture effects of microscopic damage by using the theory of internal variables. Different models have been developed to permit the damage prediction in composite structures under loading. Ladeveze and Dantec, [11], formulated mesomechanical damage model for single-ply laminate considering as composite damages fiber/matrix debonding and matrix microcracking; these
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damage modes are represented by two internal (damage) state variables; the damage evolution is then governed by a law assumed to be a linear function of equivalent damage energy release rate. Xiao et al., [12] and [13] used this approach in modelling energy absorption of composite structures in crashworthiness applications and to study damage during quasistatic punching of woven fabric composites; Williams and Vaziri, [14], used damage mechanics principles along with matrix and fiber failure criteria to model damage due to low-velocity impacts; Yen and Caiazzo, [15], implemented a damage model (MAT 162) in LS-DYNA by generalizing a layer failure model that already existed (MAT 161); their damage model is based on damage mechanics approach due to Matzenmiller et al., [16], and it incorporates progressive damage and softening behavior after damage initiation. This model will be analyzed subsequently and then implemented as material subroutine in FORTRAN code for the commercial finite element software ABAQUS for single integration point brick elements only. It will be used in progressive failure analyses on single element. 1.1.3. The continuum damage mechanics: a damage constitutive model As seen previously, progressive failure models are a combination of failure criteria (which indicates if failure has occurred and what is the mode of failure) and post failure degradation rules. The simple rule uses knockdown factors close to zero; the more complex rule uses gradual unloading based on CDM. A schematic presentation on the different degradation models and their influence on the finite element level stress strain curve is shown in Figure 2. The continuum damage mechanics theory allows to represent the damage state of a material in terms of properly defined state variables (or damage variables) and to describe the mechanical behaviour of the damage material and the further development of the damage by the use of these state variables, [17]. The term damage is used to indicate the deterioration of the material capability to carry loads. From a general point of view, damage develops in the material microstructure when non-reversible phenomena such as microcracking, debonding
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between the matrix and the second phase particles, microvoid formation take place [18]. Kachanov, [19], pioneered the subject of damage mechanics by introducing the concept of effective stress. This concept is based on considering a fictitious undamaged configuration of a body and comparing it with the actual damaged configuration. The damage variable is defined in terms of both the damaged and effective cross-sectional areas of the body. Kachanov, [19], originally formulated his theory by using simple uniaxial tension. Following its work, a cylindrical bar subjected to a uniaxial tensile force F, as shown in Figure 3, is now considered.
Damaged state (0
