Mean damage parameter for the characterization of fatigue cracking behavior in bituminous mixes

The optimization of the laboratory mix design is crucial to improve the performance of the asphalt mixes during its service life. For this purpose it is necessary the use of tools that can efficiently measure the mechanical response of these materials. Fatigue cracking is one the main distresses that occurs in pavements around the world. During the laboratory tests, this phenomenon is difficult to characterize because of its heterogeneous nature (disperse in the three dimensions and random). In order to improve the characterization of the fatigue cracking behavior of asphalt mixes, this research proposes a new parameter (Mean Damage Parameter), which combines the dissipated energy concepts and the phenomenological approach (number of cycles which cause its fail). This paper shows the basics of this parameter, and the results obtained in a study carried out to evaluate its efficiency as a tool for the improvement in the laboratory mix design.     

Fracture mechanics of idealised bituminous mixes

The durability of asphalt pavements is strongly impaired by cracks, caused primarily by traffic loads and environmental effects. In this work, fracture behaviour of idealised asphalt mixes is investigated. Experiments on idealised asphalt mixes under pure-tension mode (mode I cracking) were performed and fracture parameters were evaluated. In these three-point bend fracture tests, the test variables were temperature and load rate. The test data were stored in an asphalt materials database and special-purpose tools were implemented to analyse and handle the laboratory data automatically. Fracture mechanism maps were constructed, showing the conditions associated with ductile, brittle and ductile–brittle transition regimes of behaviour. The mechanism maps show the failure response of the material in terms of the stress intensity factor, strain energy release rate and J-integral as a function of the temperature-compensated crack mouth opening strain rate. Fracture behaviour of asphalt mix specimens was simulated by cohesive zone model in conjunction with a novel material constitutive model for asphalt mixes. The finite element model agrees well with the experimental results and provides insights into fracture response of the notched asphalt mix beam specimens.     

An inverse approach to determine the constitutive model parameters from axial crushing of thin-walled square tubes

Knowledge of the behaviour of structural components is essential for their design under crash consideration. Constitutive models describe their material behaviour in finite element (FE) codes. These constitutive models are in relation to the material parameters which have to be determined. The strain rates commonly observed in crash events are in the range of 0–500 s^-1. Classic experimental devices such as Hopkinson’s bars do not easily cover this range of strain rates. An inverse numerical approach based on the experimental quasi-static and dynamic axial crushing of thin-walled square tubes has therefore been developed to determine the constitutive model’s parameters. The inverse method is applied in this paper in two stages to determine the power type elastic–plastic constitutive model’s parameters and the Cowper–Symonds constitutive model’s parameters. The identified power law is compared with the results obtained by quasi-static tensile tests and shows that the identified parameters are intrinsic to the material behaviour. The Cowper– Symond’s parameters identified by this method are then used in FE simulation to predict the dynamic response of the same square tube subjected to bending loading. The results obtained show a good correlation between the experimental and numerical results.     

New simplified approach for obtaining a reliable plateau value in fatigue analysis of bituminous materials

The Plateau Value (PV) based on the Ratio of Dissipated Energy Change (RDEC) approach has been proven to provide a unique relationship with the fatigue life, N_f, independent of loading mode, temperature and frequency. In this paper, a new simplified approach is proposed to compute the unique energy parameter PV. The results of this study show that applying the proposed method allows a unique fatigue power law to be produced and eliminates the ambiguity and variability in calculating PV. However, the study also shows that the PV-N_f fatigue curves for bituminous materials are dependent on material type which is contradictory to other studies dealing with PV. The study also highlights the importance of appropriately identifying the fatigue failure point prior to commencing any fatigue analysis.     

An inverse problem approach to optical homodyne tomography

Abstract

The problem of optical homodyne tomography is considered in the context of a Bayesian model-fitting or inverse problem approach. An algorithm is formulated, based on matrix computation rather than the numerical approximation of an analytic inverse transform. This automatically takes into account the effects of noise, detector inefficiencies and incomplete sampling of the data. The relationships with conventional reconstruction schemes, methods for including various forms of prior information and for calculating error estimates are discussed. The process of reconstructing the photon number distribution and the density matrix are illustrated using both simulated and experimental data.     

Potential of fire extinguisher powder as a filler in bituminous mixes

Fire extinguishers must be maintained at regular intervals and many problems arise when fire-resistant dry powders need replacement. We analyze the potential of fire extinguisher powder (termed REP) as a filler in bituminous mixes. REP and REP-admixed bituminous mixes were subjected to chemical analysis, and the mechanical properties and environmental performances of the mixes were tested. Mixes with different REP contents were prepared. Mechanical performance was adequate and environmental compatibility was achieved. Practical applications and perspectives in rehabilitation, maintenance, and research are outlined.     

Three‐dimensional analysis of fatigue tests on bituminous mixtures

A tension–compression test on cylindrical specimens was used to study the three‐dimensional behaviour of bituminous mixtures during fatigue tests. The tests were carried out at 10 °C, 10 Hz at constant strain amplitude mode. The axial strain, radial strain and axial stress were measured using a prototype apparatus developed at the University of Lyon/“Ecole Nationale des TPE” (ENTPE). In addition to axial stress and strain analysis, the measurements of the radial strain made it possible to obtain the complex Poisson ratio and the volumetric strains during the tests. The results showed good correlations between the volumetric strains and global damage. The effects of the change of temperature due to viscous dissipation on the volumetric strain and on the complex modulus were also analysed.     

Evaluation of fatigue properties of bituminous binders

The original asphalt binder Superpave specification criteria for fatigue, G^*sinδ, has received considerable criticism as a specification requirement. A time sweep using the dynamic shear rheometer (DSR) has been proposed as an alternative test method for the Superpave specification. The “modulus versus number of cycles” relationships generated in the time sweep test have the appearance of typical fatigue curves. In this paper, the data was examined with respect to its validity as measure of fatigue. Special attention was given to parameters that affect or could be confounded with “true” fatigue response: apparent fatigue can generate phenomena susceptible to interfere with the fatigue behavior:

An engineering approach to fatigue analysis based on elastic‐plastic fracture mechanics

Nowadays cast iron components are widely used in highly stressed structures. Component lifetime is strongly influenced by inhomogeneities caused by the material's microstructure and the manufacturing process (graphite particles, (micro‐)shrinkage pores, inclusions). Inhomogeneities often act as a fatigue crack starter. Lifetime until failure may be divided into stages for crack initiation, short and long crack growth. Initiation of a crack of technical size (a ≈ 1mm) is often dominated by the growth of short cracks. The paper presents an approach to analyse the mechanically short fatigue crack growth based on elastic‐plastic fracture mechanics considering the closure behaviour of short cracks. The effective J‐integral range is used as a crack driving force. Finite element analysis results as well as analytical solutions to approximate the crack driving force are presented. The application of the approach is successfully demonstrated for cast iron material EN‐GJS‐400‐18‐LT using data from fatigue tests, microstructure and fracture surface analyses to assess the fatigue life.     

Evaluation of the compactability of bituminous emulsion mixes: experimental device and methodology

Laboratory asphalt mix design methodologies are aimed at predicting behaviour and determining characteristics of mixes. The French laboratory methodology for bituminous mixes is partially devoted to a compactability assessment. Samples are characterised by tests using the gyratory compactor. In this test, loose material is submitted to simultaneous compressive and shear forces, which lead to an internal aggregate reorganisation. The current French experimental device, called ‘PCG3’, was devoted strictly to hot mix asphalt characterisation. At present however, compactability properties of emulsion-treated gravel also appear as critical information due to the growing interest in bituminous cold mixes within an environmentally friendly context. A research project has been conducted in order to adapt the current ‘PCG3’ to allow for the compaction of cold mixes by adding the functionality of collecting extruded water due to emulsion breaking. This article is intended to describe this new device and determine the influence from adjusting parametric sensitivity on gravel treated with emulsion and compactability behaviour.     

An approach to fatigue life modeling in titanium-matrix composites

A review of the procedures developed by the author and his colleagues over the last several years for predicting elevated-temperature fatigue life of metal-matrix composites is presented. Modeling approaches involve concepts of both linear and non-linear summation of damage from cycle-dependent as well as time-dependent mechanisms. The analyses, further, treat the micromechanical stresses in the constituents as parameters in the life prediction models. The material characterized is SCS-6/Timetal®21S, a metastable beta titanium alloy reinforced with continuous SiC fibers. Modeling is applied to isothermal fatigue at different frequencies and temperatures, and thermomechanical fatigue (TMF) under both in-phase and out-of-phase loading conditions at different temperature ranges and maximum temperatures. Experimental data are used as the basis for determining the parameters embedded in the models. The numerical results, in turn, provide insight into the dominant mechanisms controlling fatigue life under a given condition. The capability to correlate experimental data from a wide variety of test conditions for several versions of a damage summation model is demonstrated.     

Application of inverse analysis to determine the strain distribution with optoelectronic method insensitive to temperature changes

This paper presents the application of inverse analysis to determine the stress distribution in a way that is insensitive to changes in temperature. For this purpose, a sensor with a fiber Bragg grating (FBG) was used. The paper discusses the direct solution of the task and presents the development and validation of a mathematical model of the Bragg grating sensor. Computer simulations were performed to apply numerical algorithms that completed the calculations according to the mathematical structure of the model and considered the values of all other elements of the FBG sensor. An experimental study was also conducted using a constructed measuring post.     

An inverse approach for pressure load identification

An inverse approach for the identification of pressure loading on a structure has been proposed and developed. In this approach, surface measurements of structural response (e.g. strain, displacement and velocity field measurements, such as can be measured with 3D digital image correlation) are utilized as input data and are combined with numerical simulations to identify the pressure load on a structure. The inverse approach has been verified by numerical benchmarks involving pressure identification under quasi-static as well as dynamic impulse loading conditions, and also been validated by an experiment involving a quasi-static pressure load. The results indicate that the proposed inverse method can identify not only the magnitude of the quasi-static pressure but also the impulsive pressure loading history. The developed inverse approach offers an opportunity to apply inverse analysis techniques to identify interactive pressure loads (such as those resulting from a blast wave) on structures in explosive events.     

An inverse analysis approach of the Erichsen test starting from a finite element model

During the deep drawing process the deformation history is different as compared to the tensile one where the constitutive equation can be identified only for small values of the plastic strain. More accurate values of the constitutive parameters can be obtained using the Erichsen drawing test. In this work we propose to use the inverse analysis principle to identify the rheological parameters directly from the Erichsen test. Results obtained for classical steel will be analyzed using an identification numerical high board (OPTPAR) automatically coupled with a commercial finite element code charged to simulate numerically the experimental test. Application to a DC03 sheet steel alloy will be presented.     

An inverse variational inequality approach to the evolutionary spatial price equilibrium problem

It is well known that the time-dependent spatial price equilibrium problem can be transformed into and studied as an evolutionary variational inequality. However, in some situations, control policies may be imposed to the end of regulating the amounts of production and consumption. As a consequence, the problem becomes a time-dependent spatial price equilibrium control problem and is formulated as an evolutionary inverse variational inequality. The existence of solutions is then investigated and a numerical example is also provided.     

An invariant-based approach for high-cycle fatigue calculation

Fatigue failures of in-service components are frequently due to multiaxial loadings; therefore, damage quantification in such conditions is important to many industrial applications. In this work a multiaxial criterion suitable for high-cycle fatigue assessment is formalized. It makes use of hydrostatic stress component and deviatoric stress component to estimate fatigue damage. A new formulation for the equivalent amplitude of the deviatoric component is formalized and compared with definitions proposed by Deperrois and Li and De Freitas. Damage evaluation procedure is discussed for deterministic loads and explicit analytical formulation is presented for sinusoidal loadings. Fatigue criterion is applied to experimental data taken from literature, related to several materials subjected to either in-phase or out-of-phase loads. It is shown that the new approach gives good predictions for both smooth and notched specimens. A similar comparison between experimental and theoretical results is also presented for other common criteria. It appears that the quality of the fatigue assessments obtained with the present criterion is better or, at most, similar to that of the other criteria analysed.     

A low-cycle fatigue approach to fatigue crack propagation

The damage accumulation hypothesis is used to derive a fatigue crack growth rate equation. The fatigue life of a volume element inside the plastic zone is evaluated by using low-cycle fatigue concepts. Crack growth rate is expressed as a function of cyclic material parameters and plastic zone characteristics. For a given material, crack growth increment, is predicted to be a fraction of the plastic zone size which can be expressed in terms of fracture mechanics parameters,K andJ. Hence, the proposed growth rate equation has a predictive capacity and is not limited to linear elastic conditions.     

An energy approach to fatigue tests and crack initiation stage determination

The paper deals with the strain energy consumed in fatigue failure under sinusoidal loading. The damage stress is considered, and it is shown that an energy formulation can be given for the traditional interpretation of the fatigue test results. That approach is used in determining the position of the French line, which it is suggested should be taken as the end of the crack initiation stage. The French line is constructed from the same data as used for constructing the fatigue curve.Translated from Problemy Prochnosti, No. 2, pp. 19–27, February. 1994.