Similitude Parameter Research Articles

A proposal for similitude in characterizing fatigue delamination behavior with fibre bridging of carbon-fibre reinforced polymer composites

Methods based on fracture mechanics have been widely used in fatigue delamination growth (FDG) characterization of composite laminates. These methods are based on the similitude hypothesis. It is therefore important to have appropriate parameters to well represent the similitude, which is useful for fatigue delamination test standard development aimed by Technical Committee 4 of the European Structural Integrity Society (ESIS TC4) and the ISO/TC61/SC13. In the present study, discussions on similitude parameters for fibre-bridged fatigue delamination interpretation have been conducted via fatigue data with fibre bridging at different R-ratios. The results clearly demonstrate that the strain energy release rate (SERR) indeed applied around the crack front, rather than the total applied SERR, should be employed to represent the similitude for FDG interpretation with large-scale fibre bridging. Particularly, the use of Δ√Gtip can well determine fibre-bridged delamination behavior of a given R-ratio, but it is not valid for FDG at different R-ratios in accordance with the similitude principles. A new similitude parameter, in terms of both Δ√Gtip and the maximum SERR Gmax_tip, was therefore proposed to appropriately represent FDG behavior with fibre bridging at different R-ratios. This study can not only provide database, but also give important insights for the development of mode I fatigue delamination test standard of composite laminates.

Thoughts on the Importance of Similitude and Multi-Axial Loads When Assessing the Durability and Damage Tolerance of Adhesively-Bonded Doublers and Repairs

Adhesively bonded doublers and adhesively bonded repairs are extensively used to extend the operational life of metallic aircraft structures. Consequently, this paper focuses on the tools needed to address sustainment issues associated with both adhesively bonded doublers and adhesively bonded repairs to (metallic) aircraft structures, in a fashion that is consistent with the building-block approach mandated in the United States Air Force (USAF) airworthiness certification standard MIL-STD-1530D and also in the United States (US) Joint Services Structural Guidelines JSSG-2006. In this context, it is shown that the effect of biaxial loads on cohesive crack growth in a bonded doubler under both constant amplitude fatigue loads and operational flight loads can be significant. It is also suggested that as a result, for uniaxial tests to replicate the cohesive crack growth seen in adhesively bonded doublers and adhesively bonded repairs under operational flight loads, the magnitude of the applied load spectrum may need to be continuously modified so as to ensure that the crack tip similitude parameter in the laboratory tests reflects that seen in the full-scale aircraft.

Fatigue delamination behavior in composite laminates at different stress ratios and temperatures

This study provides an investigation on mode I fatigue delamination growth (FDG) with fibre bridging at different R-ratios and temperatures in carbon-fibre reinforced polymer composites. FDG experiments were first conducted at different temperatures of R-ratios 0.1 and 0.5 via unidirectional double cantilever beam (DCB) specimens. A fatigue model, employing both the strain energy release rate (SERR) range and the maximum SERR around crack front as similitude parameter, was proposed to interpret FDG behavior. The use of this model can collapse FDG data with fibre bridging at different R-ratios into one master curve, obeying well with the similitude principles. Accordingly, it was found that FDG can accelerate with elevated temperature, but decrease at sub-zero temperature. Furthermore, there are strong correlations between the fatigue model parameters and temperature using this model in FDG interpretations. Taking these correlations into account can extend the model to accurately predict FDG behavior of other temperatures. Fractographic examinations demonstrated that temperature has effects on the FDG damage mechanisms. Both fibre/matrix interfacial debonding and matrix brittle failure were observed in FDG of −40℃. Fibre/matrix interfacial debonding becomes the dominant failure in FDG of RT and 80℃. No obvious difference on the fracture morphology was identified for FDG at different R-ratios of a given temperature.

Examining slow crack growth metrics and competing failure modes in IM7/5320-1 carbon fiber reinforced polymer laminates with pre-existing damage states

The growing use of composites in aircraft structures has necessitated a slow growth criteria to assess the life of these materials and an appropriate similitude parameter. Due to the simplified stress state and inherent interactions of intralaminar and interlaminar damage progression in multi-directional ply layups, there have been questions about the applicability of double cantilever beam specimens to aerospace applications. This study examines these interconnected damage growth mechanisms in [±453]s and [±452/902]s layups via compact tension specimen geometries, with and without pre-existing damage, in order to examine the efficacy of proposed similitude parameters in capturing slow crack growth. The change in stored potential strain energy per cycle provided the most unified results across the 18 tests under different loading and pre-existing damage conditions. Via microscopy of the specimens after damage progression, the similitude parameters were connected to overall trends in the damage mechanisms. The fatigue results, coupled with the microscopy of the interactions amongst the complex damage mechanisms, demonstrates the need to analyze proposed similitude parameters across various sample geometries and stress states, which will be more enable an understanding of composite material fatigue performance in aerospace applications.

The influence of carbon-glass/epoxy hybrid composite under mode I fatigue loading: Hybrid fiber bridging zone model

A mechanistic model for mode I fatigue delamination growth based on the hybrid fiber bridging zone was developed and is described herein. The model is based on the microfracture mechanisms of striation, fiber peel-off and fiber bridging stress, measured through scanning electron microscopy analysis. The effects of the carbon and glass fiber delamination features at the microscopic level were also considered to predict the crack propagation behavior in a hybrid laminate. The experimental SERR based on the fiber bridging zone model was used as the similitude parameter for the crack growth rate, following power law.

A unified performance conversion method for similar compressors working with different gases based on polytropic analysis and deep-learning improvement

The similitude method for compressors working with different gases makes it possible to obtain the performance map of a gas compressor through the experiment of a similar air compressor, which thereby largely simplifies the test rig and saves the cost. Existing similitude methods choose isentropic efficiency as the similitude parameter, which cannot take into account all the impact factors (e.g. the real-gas effect) in the performance conversion, thus resulting in limited applications. In this paper, the similitude parameter for efficiency is theoretically deduced by analyzing the essential polytropic compression process. It is proved that polytropic efficiency serves as a more unified similitude parameter than isentropic efficiency. On this basis, a unified performance conversion method is first proposed and then validated. Results show that the unified method can be applied to all kinds of gases, including incompressible gases, ideal gases, and real gases. Relative errors in the performance conversion are less than 4% for weak real-gas-effect gases while about 6% for strong real-gas-effect gases. To further reduce the errors for strong real-gas-effect gases, two correction coefficients are introduced and deep learning technology are adopted to predict their values. It is validated that errors can be reduced to less than 2% by the deep-learning improvement.

Crack growth in adhesives: Similitude and the Hartman-Schijve equation

Structural adhesives are widely used for joining composite components in many industries and crack growth in such materials is far more likely to occur when they are subjected to repeated cyclic loading than to monotonic loading. Whilst the Hartman-Schijve equation for fatigue crack growth (FCG) has been shown to hold for cohesive crack growth in adhesives under Mode I, Mode II and Mixed-Mode I/II loading, little attention has been paid to its ability to capture the effects of the thickness of the adhesive layer or the test temperature. The present paper examines FCG, that occurs cohesively through the adhesive layer, in two toughened epoxy adhesives typical of those used in the automotive and the aerospace industries. Firstly, it is established that when the FCG rate, da/dN, curves are expressed as a function of Δ√G, or ΔG, where G is the energy release-rate, then the crack growth curves are a function of the thickness of the adhesive layer. It is then shown that this dependency vanishes when da/dN is expressed as a function of the crack-driving force, Δκ, as defined by the Hartman-Schijve equation. Secondly, it is shown that similar observations are recorded when the effects of test temperature are considered. Therefore, it is suggested that the parameter Δκ appears to be a valid similitude parameter.

A novel total fatigue life model for delamination growth in composite laminates under generic loading

It is really important to have a reliable model to represent fatigue delamination growth (FDG) behavior for composite structural design and life evaluation with the wide applications of composites in aerospace industry. Therefore, a new total fatigue life model for delamination growth in composites has been proposed for engineering in present study, according to introducing a new crack similitude parameter and using the total life strategy. It clearly demonstrates that the FDG behavior under various fatigue loading conditions in the entire strain energy release rate (SERR) range can be appropriately characterized with this model. Particularly, a master resistance curve can be obtained to determine the FDG behavior under various R-ratios at a given mode mixity. And these resistance curves can shift downwards with mode mixity. This model will be important for material characterization, comparison and development, which is prerequisite for the applications of the damage tolerance philosophy in composite structural design and life evaluation of a composite structure.

Experimentally Derived Thresholds for Windblown Sand on Mars

AbstractAeolian sand transport frequently occurs on Mars despite wind speeds rarely exceeding predicted thresholds for motion. This dissonance is problematic for understanding aeolian processes and the resulting geomorphologic responses in contemporary and ancient atmospheres. To address the apparent discrepancy between speeds required to initiate sand motion and transport observed from orbital and in situ observations, we conducted a series of wind tunnel experiments at Martian atmospheric pressures and used buoyancy as the similitude parameter to simulate the force required to initiate particle motion on Mars. Shear velocities were derived from velocity profiles corresponding to the onset of sporadic transport, which can induce downwind cascading motion. Here, we find that threshold shear velocities are slower than previously thought by a factor of 1.6 to 2.5. Measured wind speeds on Mars exceed our observed thresholds, thus offering one mechanism behind the dissonance between observations of transport below previous thresholds of motion.

Numerical study of bluntness effects on laminar leading edge separation in hypersonic flow

Bluntness effects on laminar hypersonic leading edge separation are investigated numerically at Mach number $M\approx 10$, unit Reynolds number $Re=1.3\times 10^{6}~\text{m}^{-1}$, specific enthalpy $h_{o}=3.1~\text{MJ}~\text{kg}^{-1}$ and wall-to-stagnation temperature ratio $T_{w}/T_{o}=0.1$. Such effects are important from an experimental point of view and because bluntness can affect a separated flow favourably or adversely. In this study, two blunt leading edge cases of small radius ($15~\unicode[STIX]{x03BC}\text{m}$) and large radius ($100~\unicode[STIX]{x03BC}\text{m}$) are investigated. A comparison with the idealised sharp leading edge case is also given. General flow features and surface parameters such as the shear stress, pressure and heat flux are presented and analysed. The results have also been interpreted in terms of Cheng’s displacement-bluntness similitude parameter affecting the size of separation. Previous experiments by Holden delineated small and large bluntness effects based on Cheng’s parameter and considering small to moderate separated regions. In this study, leading edge separation was found to suppress the favourable effect of bluntness in delaying separation. Bluntness, furthermore, seemed to promote the appearance of secondary vortices within a main separated region. Analysis of reverse flow boundary layer profiles such as velocity, pressure and temperature is also given. It is shown that bluntness accentuates large transverse gradients. This in turn adversely effects the reverse flow boundary layer leading to the appearance of secondary vortices.

Using approximate similitude to design dynamic similar models

Abstract This research deals with the analysis of approximate similitude between the dynamic similar models and the full-scale prototype of an aircraft. Due to physical and technical constraints, a full dynamic similarity is not practically possible and previous works have all neglected one or two similarity criteria like Mach or Reynolds numbers for the sake of Froude number similarity. In this work, it is shown that Mach number has an important effect on aerodynamic characteristics and dynamic response of an aircraft and that neglecting it makes the generalization of the scale-model test data invalid for the full-scale prototype. In order to address this problem, a measurable quantity named approximate similitude parameter is proposed, which takes into account both dynamic similarity criteria and the scale model test objectives. The effectiveness of this parameter is shown by a case study to find out optimal weight, moments of inertia and velocity for the scale model to achieve optimal dynamic similarity.

Thickness effects on fibre-bridged fatigue delamination growth in composites

This paper provides an investigation on thickness effects on fibre-bridged fatigue delamination growth (FDG) in composite laminates. A modified Paris relation was employed to interpret experimental fatigue data. The results clearly demonstrated that both thickness and fibre bridging had negligible effects on FDG behaviors. Both energy principles and fractography analysis were subsequently performed to explore the physical reasons of this independence. It was found that the amount of energy release of a given crack growth was not only independent of fibre bridging, but also thickness. Fibre print was the dominant microscopic feature located on fracture surfaces, physically making the same energy dissipation during FDG. Furthermore, the present study provides extra evidence on the importance of using an appropriate similitude parameter in FDG studies. Particularly, the strain energy release rate (SERR) range applied around crack front was demonstrated as an appropriate similitude parameter for fibre-bridged FDG study.

Mode I fatigue delamination growth with fibre bridging in multidirectional composite laminates

Fatigue delamination in multidirectional composite laminates was experimentally investigated in present study. Both the Paris relation and a modified Paris relation (with a new similitude parameter) were employed to interpret fatigue delamination with significant fibre bridging. The results clearly demonstrated that fatigue delamination was independent of fibre bridging, if a reasonable similitude parameter was used in data reduction. As a result, a master resistance curve can be fitted to determine fatigue crack growth with different amounts of fibre bridging. The energy principles were subsequently used to provide physical interpretation on fatigue delamination. The results indicated the energy release for the same fatigue crack growth remained constant with fibre bridging. Bridging fibres in most cases just periodically stored and released strain energy under fatigue loading, but had little contribution to real energy release. The master resistance curve was finally applied to predict fatigue delamination with fibre bridging. Acceptable agreement between predictions and experiments was achieved, demonstrating the validation of the modified Paris relation in fibre-bridged fatigue delamination study.

A validation of a modified Paris relation for fatigue delamination growth in unidirectional composite laminates

Abstract The aim of this paper is to provide evidence on the validation of a modified Paris relation in fatigue crack growth with fibre bridging. Energy principles were first applied to investigate energy release in fatigue delamination growth. A comparison between the Paris and the modified Paris relations was completed subsequently. The application of the Paris relation can artificially cause different resistance curves of fatigue delamination with fibre bridging, violating the hypothesis of similitude and the energy dissipation results. However, the use of the modified Paris relation can result in a master resistance curve, which is physically consistent with the law of similitude and the energy release regulations. This derives from using an appropriate similitude parameter in data reduction. It is therefore reasonable to use the strain energy release rate (SERR) actually applied on the crack front, rather than the total applied SERR, as similitude to correlate fatigue crack growth. The master resistance curve was finally employed to predict fatigue results from literature. Acceptable agreement between predictions and experiments was achieved, validating the effectiveness of the modified Paris relation in determining fatigue crack growth with fibre bridging.

Understanding mixed-mode cyclic fatigue delamination growth in unidirectional composites: An experimental approach

Due to the lack of fundamental knowledge of the physics behind delamination growth, certification authorities currently require that composite structures in aircraft are designed such that any delamination will not grow. This usually leads to an overdesign of the structure, hampering weight reductions. In real structures, delaminations tend to grow under a mix of modes I and II. Although some studies have tried to assess mixed-mode fatigue delamination, little progress was made in understanding the physics behind the problem. Therefore, this work scrutinizes mixed-mode fatigue delamination growth and examines experimentally the damage mechanisms that lead to fracture. To this aim, mixed-mode delamination fatigue tests were performed at different mode mixities, displacement ratios and maximum displacements. Selected fracture surfaces were analysed after the tests in a Scanning Electron Microscope to gain insight on the damage mechanisms. The physical Strain Energy Release Rate G∗ was used as the similitude parameter, enabling the characterization of fatigue mixed-mode delamination propagation. The results obtained show no displacement ratio or maximum displacement dependence. Furthermore, the energy dissipated per area of crack created is approximately constant for a given mode mixity. However, the analyses of the fracture surfaces and the correlation of the damage features with energy dissipation indicate that different damage mechanisms that might be activated under different loading parameters cause the resistance to delamination to change under a given loading mode.

On the physical interpretation of the R-ratio effect and the LEFM parameters used for fatigue crack growth in adhesive bonds

The available models for the prediction of fatigue crack growth in adhesive bonds rely on the similitude principle. In most cases, one of three similitude parameters based on the strain energy release rate (SERR) is used; i.e. Gmax,(ΔG)2, or ΔG. In all cases it is usually observed that keeping the similitude parameter constant, and changing the R-ratio, results in a different crack growth rate. In this paper it is shown that this apparent ‘R-ratio’ effect is caused because the selected similitude parameter does not define a unique load cycle; a single value of the similitude parameter could correspond to infinitely many load cycles. The strain energy dissipation approach is used to show that the resistance to fatigue crack growth is related to the maximum applied load. The amount of energy available for crack growth is shown to be related to the applied cyclic work. With these relationships the R-ratio effects reported in literature can be qualitatively explained, purely in terms of the actual applied load cycle. Although it is possible that the material behaviour also depends on the R-ratio, the magnitude of these effects can only properly be determined if the applied load cycle is correctly described first.

Electrolyte Flow in an External Magnetic Field: A Dimensionless Analysis

In this paper, some recent work on the flow induced by an external magnetic fields acting on electrochemical cell is reviewed. Although the influence of the magnetic field on the hydrodynamics has been studied for over 5 decades, the magnetohydrodynamics (MHD) remains relatively unfamiliar to all but a few research groups. There are nearly a countless number of dimensionless parameters in electrolytic flow (bubble induced flow) and MHD, but they have been introduced for convenience by different authors. The similitude parameter proposed by Solheim, Johansen, Rolseth, and Thonstad (1989) and Perron, Kiss, and Poncsak (2006) have been modified to provide a full set of parameters for electrolytic cell operating under external magnetic field. The bubble sliding characteristics underneath an inclined plane are studied using copper sulphate solution (as an electrolyte) in lab-based-scale and discussed.

PIV Measurements of Air Distribution in a Reduced-Scale Model - Ventilation of a Busbar Corridor in a Hydropower Station

On the basis of modelling with similarity theory and by using the Archimedes number, Ar, as the similitude parameter, this paper analyzes the air distribution of a busbar corridor in a hydropower station by using the Particle Image Velocimetry (PIV) measurement technique. The measurements were conducted in a 1:50 scale model for nine different operating conditions, including three air supply rates: 0.75G0, G0, 1.25 G0 and three heat release rates: 0.75Q0, Q0, 1.25 Q0 (G0 and Q0 are design values). The variation regularity of air distribution for the nine conditions were analyzed and evaluated based on the following aspects: the airflow pattern in the busbar corridor, the efficiency of energy utilization and the uniformity of air velocity and air temperature in the occupied zone. The experimental results show that the confluence of two air supply jets forms a cold airflow attached on the ground of the occupied zone, and that the attached distance increases with larger modified Archimedes number ArQ. For air temperature increasing in the air supply direction, the maximum temperature increase appears at the outlet and is 5 °C, while the minimum temperature increase appears at the inlet and is 2 °C. Moreover, the energy utilization coefficient η in Case 5 is the largest compared with other cases, which illustrates that good economical efficiency in the model can be obtained by choosing 0.2 m/s as the air supply velocity when the heat release rate is 7.4 W. The experimental data of this research provide a useful reference for ventilation system design for similar types of underground buildings.

Complex Aerodynamics Behavior of High Spin APFSDS Projectile

The supersonic aerodynamics of a high spin armor-piercing fin-stabilized discarding sabot projectile (APFSDS) is numerically and experimentally investigated. Classically, using a 120 mm smooth bore gun, the value of the nondimensional steady spin rate of the inflight APFSDS projectile is about 0.01. In our case, a medium caliber APFSDS projectile is fired using a rifled barrel gun. The initial nondimensional spin rate, which is, with the Mach and the Reynolds numbers, the third similitude parameter governing the projectile aerodynamics, is significantly greater and about 0.09. Complex aerodynamics and flight dynamics were found and are detailed in the paper. In particular, the side force and moment evolutions with spin rate and angle of attack reflect a highly nonlinear behavior of the Magnus effect. The numerical predictions are mainly based on Reynolds-averaged Navier–Stokes (RANS) and URANS (Unsteady RANS) equations. Flight tests have been performed in an aeroballistics corridor. The exterior ballistics of the projectile was investigated using a yaw cards method, the experimental results are analyzed using a 6DOF flight dynamics model. The comparison between computational fluid dynamics (CFD) computations and flight tests results is satisfactory. CFD computations show, for the first time at our knowledge, that a roll-pitch coupling may appear.

Convective heat transfer on a rotating disk with a centred impinging round jet

Flow visualisations and heat transfer measurements on a rotating disk, with a relatively small centred jet perpendicularly impinging on it, are accomplished by means of infrared (IR) thermography associated with the heated-thin-foil thermal sensor. Flow visualisations show a strong interaction between the turbulent jet and the laminar boundary layer over the rotating disk. A new governing similitude parameter is introduced and a heat transfer correlation for the Nusselt number at the disk centre is proposed. In most cases, the Nusselt number radial profiles tend to overlap if they are normalised with the Nusselt number computed by means of this correlation.