Failure analysis of variable stiffness composite plates using continuum damage mechanics models

An efficient D-vine copula-based coupling uncertainty analysis for variable-stiffness composites

A recently developed anisotropic model of continuum damage mechanics has been applied successfully to characterize ductile fracture of cracked plates under mode I and mixed mode failures. The damage model is further extended in this investigation to examine its applicability to include notch ductile fracture of thin plates containing a circular hole. Two hole sizes of 16 mm and 24 mm diameters are chosen and the specimen material is aluminum alloy 2024-T3. Fracture loads of the plates are predicted by the damage model and compared satisfactorily with those determined experimentally. This investigation provides an important confirmation that not only the anisotropic model of continuum damage mechanics but also the same failure criterion developed can be effectively employed to characterize both ductile fracture for plates containing an isolated macro-crack or circular hole which would otherwise not be possible using the conventional theory of fracture mechanics. The successful development of the unified approach to characterize ductile failure provides a vital impetus for design engineers in the general application of the theory of continuum damage mechanics to solve practical engineering problems.

For Variable Stiffness (VS) composites with steered curvilinear tow paths, the fiber orientation angle varies continuously throughout the laminate, and is not required to be straight, parallel and uniform within each ply as in conventional composite laminates. Hence, the thermal properties (conduction), as well as the structural stiffness and strength, vary as functions of location in the laminate, and the associated composite structure is often called a “variable stiffness” composite structure. The steered fibers lead not only to the alteration of mechanical load paths, but also to the alteration of thermal paths that may result in favorable temperature distributions within the laminate and improve the laminate performance. Evaluation of VS laminate performance under thermal loading is the focus of this chapter. Thermal performance evaluations require experimental and numerical analysis of VS laminates under different processing and loading conditions. One of the advantages of using composite materials in many applications is the tailoring capability of the laminate, not only during the design phase but also for manufacturing. Heat transfer through variable conduction and chemical reaction (degree of cure) occurring during manufacturing (curing) plays an important role in the final thermal and mechanical performance, and shape of composite structures. Three case studies are presented in this chapter to evaluate the thermal performance of VS laminates prior to and after manufacturing. The first case study is a numerical analysis that investigates the effect of variable conductivity within the VS laminate on the temperature and degree of cure distribution during its cure cycle. The second case study is a numerical analysis that investigates the transient thermal performance of a rectangular VS composite laminate. Variable thermal conductivity will affect the temperature profile and results are compared to a unidirectional composite. The effect of fiber steering on transient time and steady state solutions is compared to the effect of unidirectional fibers. The third case study is an experimental one that was conducted to evaluate the thermal performance of two variable stiffness panels fabricated using an Advanced Fiber Placement (AFP) Machine.

Design, manufacturing, and testing of a variable stiffness composite cylinder

The design space for high-performance lightweight composite structures has grown considerably since the advent of the variable stiffness concept. In fact, variable stiffness composites have been found to improve buckling performance and dynamic stability, and to tune the structure’s dynamic response by tailoring structural stiffness. Thus, in order to exploit this wider design space, efficient linear analysis tools have an important role in preliminary design of variable stiffness structures, enabling designers to find more effective solutions when considering prestressed dynamically excited aerospace components. Considering this, a multi-domain Ritz method for eigenfrequency, transient and dynamic instability analysis of prestressed variable stiffness laminated doubly-curved shell structures is presented. Working within the first-order shear deformation theory, Sanders–Koiter shell kinematics allow general orthogonal surfaces to be modelled without further assumptions on the shallowness or on the thinness of the structure. The efficiency of the proposed Ritz method is granted by using Legendre orthogonal polynomials as displacement trial functions, while flexibility in modelling and design is given by penalty techniques that allow stiffened variable angle tow shell structures to be modelled as an assembly of shell-like domains. The proposed approach is verified by comparison with published benchmark results and finite element solutions. Original solutions are presented for a prestressed stiffened variable angle tow shell structure, which show great accuracy with an order of magnitude fewer variables when compared to standard finite element procedures, proving the reliability and efficiency of the present method in dealing with the dynamic analysis of multi-part aerospace structures.

Novel adherend laminate designs for composite bonded joints

Professor Sadeghi and his coworkers have been developing a method to estimate the rolling contact fatigue life of rolling bearings in recent years using a continuum damage mechanics (CDM) approach. Development of the method has involved progression from a defect-free and inclusion-free model to ones incorporating grain boundary cracks and inclusions.The most recent paper on this topic is authored by Walvekar et al. [1]. In Sec. 2.2, the authors stated “It was hypothesised that failure mechanism for torsional fatigue and rolling contact fatigue are equivalent because the mechanism for damage accumulation is similar for both types of fatigue phenomena.” It is necessary to verify whether such a hypothesis is correct or not but this has not been carried out within the paper.This hypothesis was postulated by Raje and Sadeghi in 2009 in a paper published in the IMechE Journal of Engineering Tribology entitled “Statistical Numerical Modelling of Sub-Surface Initiated Spalling in Bearing Contacts” [2]. In Sec. 3, the authors stated “It is hypothesised that since fatigue damage under rolling contact conditions is caused purely by the action of shear stresses, the mechanism of failure is similar to that prevalent in torsional fatigue. Thus, by knowing the stress-life relationship for a material in torsional fatigue, the fatigue damage parameters can be extracted.”Torsional fatigue data on SAE 52100 bearing steel from Styri were used to provide the shear stress to failure [3], but Styri stated that in about 90% of cases, failures start below the surface, presumably at inclusions or other defects that act as stress concentrating features. However, the model being validated by Raje and Sadeghi is for a material free of defects, voids, or inclusions, while the steel used by Styri would be of 1940 s pedigree but with no statement of its cleanliness.Would the authors comment upon this observation, particularly as, intuitively, the torsional fatigue life of a pristine steel would be expected to be much longer than the one containing defects or inclusions while failures would be surface-initiated?Furthermore, results from the CDM model of pristine steel are compared to L10 bearing lives measured by Lundberg and Palmgren for NU 209 cylindrical roller bearings. The authors present a method in Sec. 4.3 for the conversion of L10 life in shaft revolutions to inner race stress cycles. A comparison of the model results and the bearing lives of Lundberg–Palmgren is then presented. The authors stated that “Stress-life results for this bearing are shown in Fig. 7 and are found to be in good agreement with stress-life results from the current model.”Would the authors comment upon this conclusion, taking into account that the results from the CDM model of pristine steel are being compared to bearings of 1940 s pedigree with no statement of cleanliness?In Sec. 4.2, the authors claim that the model is found to fit within the range of experimental data for cylindrical roller bearings reported by Harris and Barnsby [4]. Reference to this data appears to suggest that shaft revolutions have been plotted as opposed to stress cycles in Fig. 7. Would the authors confirm whether this is the case or not?Intuitively, a defect-free and inclusion-free model should predict lives that are much longer than both the experimental data from Harris–Barnsby and Lundberg–Palmgren. Once defects such as inclusions are introduced into the model, comparisons may then be made with the experimental data. It is necessary to model the size, number, shape, and composition of the inclusions (and other defects, such as carbide stringers) within the steels tested by Harris–Barnsby (1980 s/1990 s pedigree) and Lundberg–Palmgren (1940 s pedigree) in order to carry out such a comparison. Only at this point the claims can be made for validation (or otherwise) of the model. Would the authors comment upon this observation?It also appears that the CDM model has not been validated at lower contact stresses. It may be difficult to validate the model at contact stresses below 2200 MPa (the main region of interest for industrial machines) for the following reasons:Would the authors comment upon validation of the model at lower contact stresses?

In this study, a failure analysis of two‐serial‐bolted glass‐fiber‐reinforced epoxy composite plates was performed. To determine the influences of the joint geometry and stacking sequences on the bearing strength and failure mode, parametric studies were carried out experimentally. Three different geometrical parameters—the ratio of the edge distance to the hole diameter (E/D), the ratio of the plate width to the hole diameter (W/D), and the ratio of the distance between two holes to the hole diameter (K/D)—were considered. For this reason, the E/D, W/D, and K/D ratios were designed to range from 1 to 5, from 2 to 5, and from 3 to 5, respectively. Furthermore, the tests were performed with various preload moments (2, 3, 4, and 5 Nm) and without any preload moments (0 Nm). Because of the observed effect of the material parameters on the failure behavior, composite laminated plates were stacked in two different stacking sequences: [0°/0°/30°/30°]s and [0°/0°/45°/45°]s. The experimental results indicated that the failure response of the two‐serial‐bolted joints were strictly affected by the material parameters, geometrical parameters, and values of the applied preload moments. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Refractory ceramics used as kiln furniture are designed to operate at elevated temperatures with a high thermal shock resistance. In practice, however, the material fails due to thermal fatigue after a limited number of cycles. To predict this failure behaviour, it is generally not possible to use linear elastic fracture mechanics due to the fact that the coarse grained, porous material shows a dissipative mechanical behaviour. Differently sized specimens are tested to determine the size effect associated with this material. Four different finite element models widely used for concrete modelling are investigated on their ability to describe this nonlinear failure behaviour, in particular the associated size effect phenomenon. The results of the initially promising Nonlocal Continuum Damage Mechanics (CDM) model indicate that this approach cannot properly describe the observed size effect. The other three models (Adapted Local CDM, Fictitious Crack and Smeared Crack), however, give comparable results with a good description of the observed size effect phenomenon.

Use of Damage-based Mesh Adaptivity to Predict Ductile Failure in Blast-loaded Aluminium Plates

It is well known that fabrication processes inevitably lead to defects in the manufactured components. However, thanks to the new capabilities of the manufacturing procedures that have emerged during the last decades, the number of imperfections has diminished while numerical models can describe the ground truth designs. Even so, a variety of defects has not been studied yet, let alone the coupling among them. This paper aims to characterise the buckling response of Variable Stiffness Composite (VSC) plates subjected to spatially varying fibre volume content as well as fibre misalignments, yielding a multiscale sensitivity analysis. On the one hand, VSCs have been modelled by means of the Carrera Unified Formulation (CUF) and a layer-wise (LW) approach, with which independent stochastic fields can be assigned to each composite layer. On the other hand, microscale analysis has been performed by employing CUF-based Mechanics of Structure Genome (MSG), which was used to build surrogate models that relate the fibre volume fraction and the material elastic properties. Then, stochastic buckling analyses were carried out following a multiscale Monte Carlo analysis to characterise the buckling load distributions statistically. Eventually, it was demonstrated that this multiscale sensitivity approach can be accelerated by an adequate usage of sampling techniques and surrogate models such as Polynomial Chaos Expansion (PCE). Finally, it has been shown that sensitivity is greatly affected by nominal fibre orientation and the multiscale uncertainty features.

Continuum damage mechanics elaborates the continuum mechanics-based modelling and simulation of mechanical degradation effects. The objective of this contribution is to briefly review different aspects of continuum damage mechanics of solid continua with a focus on general modelling concepts and application to isotropic as well as anisotropic damage approaches on the one hand, and to discuss possible solution strategies in the context of finite element simulations on the other. In particular, viscous regularisation and gradient-enhanced regularisation—as a reduced form of general non-local theories—are considered. Several numerical examples including ductile damage, i.e. the coupling of damage with plasticity related phenomena, are addressed which show the applicability of the particular modelling and simulation frameworks highlighted.

Experimental study and numerical simulation of adhesively bonded timber-concrete composite panels: bending behavior, adhesive shear and peel stress distributions

This work presents the experimental and finite element (FE) simulations to investigate the behavior of both unstiffened and anisogrid composite cylindrical shells subjected to low‐velocity axial impact. Impact damage has been an epidemic problem for composite structures. Even subjected to a low‐velocity impact, thin‐walled composite structures may sacrifice its load‐carrying capacity considerably due to various modes of failure. A low cost, reliable and innovative manufacturing process is proposed for the production of anisogrid cylindrical lattice structures. Initially, test coupons are fabricated as per American Society for Testing of Materials (ASTM) standards and inspected using infrared (IR) thermography to find the imperfections incurred during fabrication. The test coupons without defects were only taken into account for material characterization. FE simulations were carried out on both the unstiffened and anisogrid shells using LS‐DYNA® for a series of low‐velocity impacts. Also these shell structures were subjected to impact loading experimentally for the validation of the numerical results. The results of these studies indicate that the anisogrid model presented in this work possesses a great load‐carrying capacity than an unstiffened shell under dynamic loading conditions, also the weight of the structure has been reduced up to 51.27%. Numerical simulation results are in good agreement with the experimental data, having less than 11.56% of maximum deviation on the energy absorption value.

Design of variable stiffness composites for maximum fundamental frequency considering manufacturing constraints of tow steering