The analysis of skin-to-stiffener debonding in composite aerospace structures

A comprehensive finite element (FE) analytical tool to predict the effect of defects and damage in composite structures was developed for rapid and accurate damage assessment. The structures under consideration were curved, T-stiffened, multi-rib, composite panels representative of those widely used in aerospace primary structures. The damage assessment focussed on skin-to-stiffener debonding, a common defect that can critically reduce the performance of composite structures with integral or secondary bonded stiffeners. The analytical tool was validated using experimental data obtained from the structural test of a large stiffened panel that contained an artificial skin-to-stiffener debond. Excellent agreement between FE analysis and test results was obtained. The onset of crack growth predictions also compared well with the test observation. Since the general damage tolerance philosophy in composite structures follows the “no-growth” principle, the critical parameters were established based the onset of crack growth determined using fracture mechanics calculations. Parametric studies were conducted using the analytical tool in order to understand the structural behaviour in the postbuckling range and to determine the critical parameters. Parameters considered included debond size, debond location, debond type, multiple debonds and laminate lay-up.     

A mechanistic model for the effect of stress ratio on the LEFM fatigue crack growth behavior of metals and alloys—II. Crack-brittle materials

A recently proposed mechanistic model for the effect of stress ratio, R, on the LEFM (long) fatigue crack growth behavior of “crack-ductile” materials is extended here to explain and predict similar behavior under similar conditions of “crack-brittle” materials characterised by the presence of “static” modes of fatigue fracture in stages II and III. It is shown that in these materials the stage I behavior is similar, but the stages II and III behave differently from crack-ductile materials. Mechanism-based existence of two types of stage II curves characterised respectively by “ pure shear mode ” (SM-II) and “mixed-mode” (MM-II), both plotting linear but having different slopes, is introduced. It is shown that while stage SM-II is insensitive, stage MM-II is significantly sensitive to R, in the same material. Similar to stage I, another “ moving pivot-point ” exists at the transition from SM-II to MM-II, which slides down the “ master shear-curve ” with increasing R. Assuming a critical K_max for the initiation of static modes, a critical R for saturation of these modes, and Paris-type growth relations, a quantitative predictive model containing growth equations for stages SM-II and MM-II, has been developed. Stage III is discussed only qualitatively. Reasonably good agreement was found between predicted curves at selected R-values and a relatively large volume of experimental data for steels, Al-alloys and Ti-alloys. This simple, alternative model may be used for obtaining quick, fairly accurate and conservative estimates of R-influenced crack growth rates for design applications in preference to crack-closure which frequently requires elaborate and tedious experimental procedures.     

A uniaxial nonlinear viscoelastic constitutive model with damage for M30 gun propellant

The nonlinear viscoelastic mechanical response of a conventional tank gun propellant, M30, is modeled using a “modified superposition integral” that incorporates the effects of microstructural fracture damage. Specifically, a linear, time-dependent kernel is convolved with the first-time derivative of a power-law function of stress and a damage “softening” that accounts for damage evolution by a microcrack growth mechanism. The microcrack damage function is a master curve formed from shifted isothermal, compressive, uniaxial constant strain rate (0.01 s⁻¹ to 420 s⁻¹) data on solid, right-circular cylinders of M30 gun propellant. An attractive feature of the model is its ability to predict work-softening behavior under conditions of monotonically increasing deformation. Time-dependent predictions of stress versus time, failure stress versus failure time, and failure stress versus strain rate, quantitatively agree with experimental results from constant strain rate tests on the propellant. Theoretical predictions of time-dependent stresses for Heaviside and “ballistic-like” strain histories are also provided.     

A mechanistic model for the influence of stress ratio on the LEFM fatigue crack growth behavior of metals and alloys—I. Crack-ductile materials

Concentrating on local behavior of a highly stressed zone ahead of the crack tip, a recent mechanistic approach to analyse LEFM fatigue crack growth behavior in three stages at stress ratio R = 0 is extended here to include the effect of a positive stress ratio. This paper is limited to analysing primarily the stages I and II of “crack-ductile” materials, characterised by a purely “reversed shear” (or ductile “striation”) growth mechanism in stage II. It is shown that in these materials stage I is R-sensitive and stage II is insensitive, and these can, without invoking crack closure arguments, be rationalised alternatively by considering the dominance of a K_max-controlled “Submicroscopic Cleavage” and a ΔK-controlled “ reversed shear ” fracture mechanism, respectively. Assuming Paris type power relations to hold, a predictive model is developed that contains separate growth equations with R-effect for stages I and II and shows the existence of a characteristic “master shear-curve” and a “moving pivot-point” on this curve for a class of materials. Good agreement was found between quantitatively predicted growth curves at selected R-values and a relatively large volume of available experimental data for low strength steels, aluminum alloys and titanium alloys. Besides providing more physical explanations for the observed growth behavior, the model may also be useful as a convenient alternative to crack closure for obtaining fairly accurate and conservative estimates of fatigue life for design applications.     

Fracture-mechanics failure criteria for RC beams strengthened with FRP strips––a simplified approach

A simplified approximation approach for the evaluation of a fracture mechanics based criterion for the edge delamination failure of reinforced concrete beams strengthened with externally bonded composite materials is presented. The proposed approach is based on evaluation of the energy release rate (ERR) through the virtual crack extension method using various analytical and numerical stress analysis models. The investigated models include the high-order model, two types of “elastic foundation” or “springs” models, a simplified beam model, and finite elements analysis. The stress and displacement fields, the governing equations and their closed form solutions, and the expressions for the release rate of the total potential energy of the various models are presented. The proposed approach sets up the basis for an energetic failure criterion, in which the ERR is compared to the specific fracture energy of the bonded system. This criterion replaces the traditional allowable stress approach in describing the initiation and stable or unstable growth of the delamination crack. The capabilities of the proposed approach and its ability to evaluate the ERR through simplified and approximated models is investigated numerically. The accuracy of the simplified approach is numerically examined through comparison with the J-integral formulation. Numerical results in terms of stresses near the edge of the bonded strip, the ERR associated with initiation and growth of the interfacial crack, and the critical loads and crack lengths are presented. The paper closes with a summary and conclusions.     

A Relational Approach to Organization Design

The paper criticizes the currently dominant view of organization forms as “discrete alternatives” and “coherent” set attributes, and proposes a more refined and micro-analytic view of organization forms as particular combinations of coordination mechanisms and rights allocations. This view is relevant for understanding and devising “new” forms and proposing solutions for governing the composite and fast changing systems of today. The view is “relational” as it offers a procedure for devising “superior” configurations as combinations—relations between organizational components—in a quasi-continuous space of possibilities. The approach is sustained by the quantitative methods of network analysis as applied to relations among firm's resources and activities. Theoretically, the approach revisits organization design, integrating classic organization theory tenets with the new inputs provided by organizational economics. Substantively, it is argued that a mix of much differentiated coordination mechanisms is usually superior to the codified, “packaged”, allegedly “coherent”, forms of organization. The procedure presented in the paper is applied to a field experiment in a medium size firm.1     

Ductile fracture initiation and propagation modeling using damage plasticity theory

Ductile fracture is often considered as the consequences of the accumulation of plastic damage. This paper is concerned with the application of a recently developed damage plasticity theory incorporates the pressure sensitivity and the Lode angle dependence into a nonlinear damage rule and the material deterioration. The ductile damaging process is calculated through the so-called “cylindrical decomposition” method. The constitutive equations are discussed and numerically implemented. An experimental and numerical investigation for three-point bending tests is reported for aluminum alloy 2024-T351. Crack initiation and propagation in compact tension specimens are also studied numerically. These simulation results show good agreement with experiments. The present model can successfully predict slant fracture as well as the formation of shear lips.     

On the creep crack growth prediction by a local approach

Classical methods to predict crack growth in structures are generally based on fracture mechanics concepts. For high-temperature applications, where creep (monotonic or cyclic) or thermal stresses are present, such classical approaches lead to large difficulties. An alternative method is to calculate as accurately as possible the actual local behaviour including viscoplasticity and creep damage effects. The different levels of the possible “local approaches” are briefly reviewed and discussed; the case of creep crack growth is then studied in detail, through the use of viscoplastic constitutive equations including creep damage effect. Both the creep damage and the hardening of the metal are supposed to be isotropic, characterized respectively by the following scalar internal variables: the Kachanov's damage variable D and the cumulated viscoplastic strain p. The evolution equation of creep damage is a differential non-linear one with non-linear cumulative effect. The local states of different mechanical fields ((σ, , D) and their redistribution, due to damage effect, are accurately investigated and illustrated by various numerical examples. Finally the approach is applied to the creep of initially cracked CT specimen.     

Influence of post-buckling behaviour of composite stiffened panels on the damage criticality

In stiffened panels with defects, such as skin delaminations or stringer debonding, buckling may occur prior to the designed critical buckling load. Depending on the damage parameters, such defects may also affect the post-buckling behaviour and consequently the structural performance. An automated finite element (FE) modelling tool has been developed to predict the post-buckling behaviour of panels. It was coupled with a linear elastic fracture mechanics approach to determine damage criticality, based on the “no-growth” principle. The structural behaviour in the post-buckling range and its interaction with the damage parameters were analysed. Local buckling occurred as a result of localised stiffness reduction in the damage region. Global buckling occurred when sufficient in-plane strain was reached. The onset of local buckling was an important factor on stringer debonding criticality as the local buckling mode had an effect on the corresponding global buckling. In comparison, the onset of local buckling for the skin delamination was lower due to the thin sub-laminate separation. However, it was less influential on the damage criticality because the local buckling slowly dissipated in the far post-buckling range. It was found that the initiation of local buckling, and the interaction between the local and global buckling mode, would determine the damage criticality.     

Formation and Strength of Solid Bridges in Bulk Solids

The time consolidation of bulk solids, known as “caking,” plays an important role in many industries. To investigate the bridge formation between two discrete particles under real storage conditions a new experimental setup has been designed. In this study, the aim is to predict the caking behavior of hygroscopic materials under the influence of parameters that lead to caking phenomena. With salt-like substances such as NPK fertilizer and urea, caking increases with rising humidity and temperature. A state of matter diagram for urea shows in a condensed form the results of numerous caking experiments indicating clearly the critical caking conditions.     

Numerical interpretation of cone crack initiation trends in a brittle coating on a compliant substrate

Finite element analysis is used to interpret trends in experimentally observed critical loads for contact damage in a brittle (porcelain) coating on a compliant (polymeric) substrate. Different forms of cracking in the brittle layer—both “cone” cracking initiating at the surface, and “radial” cracking at the layer/substrate interface—are considered, with varying coating thicknesses.

The resulting predicted critical loads agree qualitatively with the experimentally observed figures. It is postulated that a previously unexplained peak in critical loads for the onset of cone cracking is caused by a transition between differing modes of cone cracking.     

A design-centered approach in developing Al-Si-based light-weight alloys with enhanced fatigue life and strength

Material heterogeneities and discontinuities such as porosity, second phase particles, and other defects at meso/micro/nano scales, determine fatigue life, strength, and fracture behavior of aluminum castings. In order to achieve better performance of these alloys, a design-centered computer-aided renovative approach is proposed. Here, the term “design-centered” is used to distinguish the new approach from the traditional trial-and-error design approach by formulating a clear objective, offering a scientific foundation, and developing a computer-aided effective tool for the alloy development. A criterion for tailoring “child” microstructure, obtained by “parent” microstructure through statistical correlation, is proposed for the fatigue design at the initial stage. A dislocations pileup model has been developed. This dislocation model, combined with an optimization analysis, provides an analytical-based solution on a small scale for silicon particles and dendrite cells to enhance both fatigue performance and strength for pore-controlled castings. It can also be used to further tailor microstructures. In addition, a conceptual damage sensitivity map for fatigue life design is proposed. In this map there are critical pore sizes, above which fatigue life is controlled by pores; otherwise it is controlled by other mechanisms such as silicon particles and dendrite cells. In the latter case, the proposed criteria and the dislocation model are the foundations of a guideline in the design-centered approach to maximize both the fatigue life and strength of Al-Si-based light-weight alloy.     

Ductile rupture in thin sheets of two grades of 2024 aluminum alloy

The damage and rupture mechanisms of thin sheets of 2024 aluminum alloy (Al containing Cu, Mn, and Mg elements) are investigated. Two grades are studied: a standard alloy and a high damage tolerance alloy. The microstructure of each material is characterized to obtain the second phase volume content, the dimensions of particles and the initial void volume fraction. The largest particles consist of intermetallics. Mechanical tests are carried out on flat specimens including U-notched (with various notch radii), sharply V-notched and smooth tensile samples. Stable crack growth was studied using “Kahn samples” and pre-cracked large center-cracked tension panels M(T). The macroscopic fracture surface of the different specimens is observed using scanning electron microscopy. Smooth and moderately notched samples exhibit a slant fracture surface, which has an angle of about 45° with respect to the loading direction. With increasing notch severity, the fracture mode changes significantly. Failure initiates at the notch root in a small triangular region perpendicular to the loading direction. Outside this zone, slant fracture is observed. Microscopic observations show two failure micromechanisms. Primary voids are first initiated at intermetallic particles in both cases. In flat regions, i.e. near the notch root of severely notched samples, void growth is promoted and final rupture is caused by “internal necking” between the large cavities. In slanted regions these voids tend to coalesce rapidly according to a “void sheet mechanism” which leads to the formation of smaller secondary voids in the ligaments between the primary voids. These observations can be interpreted using finite element simulations. In particular, it is shown that crack growth occurs under plane strain conditions along the propagation direction.     

Damage propagation in composite structural elements-coupon experiments and analyses

An overview of experiments and analyses being performed at the coupon level within the GARTEUR (Group of Aeronautical Research in Europe) action group AG16: ‘Damage propagation in composite structural elements’ is given. Both basic delamination fracture experiments such as DCB, ENF, MMB, CLS and SEN and coupon tests with embedded artificial delaminations or impact damages are carried out. The experiments are analysed using different methods and energy release rate, stress-based failure criteria and damage models are evaluated.     

On new types of non-crystalline metallic composite

The structure and mechanical properties of new types of non-crystalline metallic composites, namely “glass-quasi-crystal”, “glass-disclinated nanocrystal” and “quasi-crystal(-glass)-disclinated nanocrystal” composites are theoretically examined. In particular, a theoretical model is proposed which effectively describes the relationship between plastic deformation and the growth of the glassy phase in metallic “glass-quasi-crystal” composite materials. Here also basic features of both the structure and the mechanical properties of the “glass-disclinated nanocrystal” and “quasi-crystal(-glass)-disclinated nanocrystal” composites are theoretically examined. It is shown that such composites are characterized by a very high yield stress.     

Modeling of brittle fracture based on the concept of crack trajectory ensemble

The objective of this paper is to present a comprehensive review of an approach which stands aside from the mainstream of statistical modeling of fracture. The approach is essentially based on the concept of an ensemble of macroscopically identical fracture specimens and on averaging over it. Equivalently, an ensemble Ω of virtual crack trajectories is associated with a single specimen; the averaging is then expressed in the form of functional integration over Ω. The approach combines the concepts of weakest link theories with fracture mechanics formalism and models crack propagation through a brittle microheterogeneous solid. The statistics of microheterogeneity, e.g. the population of pre-existing defects, is reflected in a random field of specific fracture energy γ and in the statistical features of Ω. The fracture parameters employed in the approach are: parameters of the pointwise distribution of the γ-field; its correlation distance; and the characteristics of roughness of the fracture surfaces, including their fractal dimension. The probability of crack formation between any two points in a two-dimensional solid (referred to as “crack propagator”) is introduced as the main building block of the approach. It is expressed as a functional integral (over the set Ω) of the probability of crack formation along a particular path. The probability distributions of critical loads, critical crack lengths, G_1c, crack arrest locations, etc., are derived in terms of crack propagator. The dependence of the distributions on the statistical characteristics of the material as well as on the roughness of the crack trajectories is analyzed by both analytical and numerical means.     

The effects of surface preparation on the fracture behavior of ECC/concrete repair system

This paper presents the influence of surface preparation on the kink-crack trapping mechanism of engineered cementitious composite (ECC)/concrete repair system. In general, surface preparation of the substrate concrete is considered essential to achieve a durable repair. In this experiment, the “smooth surface” system showed more desirable behavior in the crack pattern and the crack widths than the “rough surface” system. This demonstrates that the smooth surface system is preferable to the rough surface system, from the view point of obtaining durable repair structure. The special phenomenon of kink-crack trapping which prevents the typical failure modes of delamination or spalling in repaired systems is best revealed when the substrate concrete is prepared to have a smooth surface prior to repair. This is in contrast to the standard approach when the substrate concrete is deliberately roughened to create better bonding to the new concrete.     

Modeling of Liquid Metal Infiltration of Porous Fiber Preform During Squeeze Casting

The present work adopts a new approach to the analytical modeling of infiltration of porous fiber preforms by liquid metal in the squeeze casting of metal matrix composites, with the assumption that the process is adiabatic and that the flow is unidirectional. Fluid dynamics is described on the basis of Darcy's law, while separate equations are derived to explain the thermal behavior of the liquid metal and the fiber, assuming that the thermal interactions between the two are interfacial. Unlike earlier models, this approach does not consider the thermal behavior of a “composite,” but instead studies the behavior of the liquid metal and the fiber preform separately. In addition to the conventional application of heat balance techniques and development of partial differential equations involving temperatures, this work introduces supplementary conditions for temperature calculations, specifically at the entry and front points during infiltration. Differential equations are solved by a method of finite differences, and the problem of additional unknowns (preform temperature) at the infiltration front position is overcome using the “virtual point” concept. Simple expressions are derived for the calculation of process parameters like total time for complete infiltration and time for solidification, on the basis of which the occurrence of complete infiltration is predicted. A novel attempt in generating the profiles of the preform and liquid temperatures at specific instants during infiltration has also been made. The relative influence of the liquid superheat temperature, the preform preheat temperature, and the squeeze pressure on the infiltration mechanism is analyzed by studying the infiltration characteristics for various squeeze conditions.     

Constraint comparisons for common fracture specimens: C(T)s and SE(B)s

New testing standards (e.g., ASTM E1921) remain under continuing development to measure the fracture toughness of ferritic steels over the ductile-to-brittle transition. The procedures assume that relatively small, deep-notch test specimens maintain near small-scale yielding conditions at fracture, which simplifies greatly the interpretation of measured values. However, 3-D finite element analyses suggest that the geometry and small size of common fracture specimens leads frequently to constraint loss, e.g., the decay of small-scale yielding conditions, at only moderate levels of deformation. The Weibull stress micromechanical model, or “local approach,” is employed here to quantify these constraint effects. Previous research along these same lines quantifies constraint loss in common fracture specimens relative to strict plane-strain, small-scale yielding conditions with a zero T-stress. Here we present a more practical approach for application within experimental testing programs by comparing directly the two most commonly tested fracture specimens, the single-edge notched bend, SE(B), and the compact tension, C(T), specimens. Developers of testing standards may thus choose a “reference” specimen then correct values measured with other specimens to the adopted reference configuration.     

On the analysis of composite structures with material and geometric non-linearities

If major weight saving is to be realised it is essential that composites be used in “primary” structural components, i.e., wing and fuselage skins. To this end it is essential that analytical tools be developed to ensure that composite structures meet the FAA damage tolerance certification requirements. For stiffened composite panels one potential failure mechanism is the separation of the skin from the stiffeners; resulting from excessive “through the thickness” stresses. This failure mechanism is also present in bonded composite joints and composite repairs. Currently failure prediction due to in-plane loading appears to be relatively well handled. Unfortunately, this is not yet true for matrix-dominated failures. Consequently, it is essential that a valid analysis methodology capable of addressing all of the possible failure mechanisms, including failure due to interlaminar failure, be developed. To aid in achieving this objective the present paper outlines the results of a series of experimental, analytical and numerical studies into the matrix-dominated failures of rib stiffened structures.