Dissipated Energy Approach Research Articles

Scanning Laser Detection System Used to Measure Propagation of Fatigue Damage of Asphalt Mixes

Fatigue damage is a major distress in pavements that has been studied extensively in various approaches, over the past two decades. It is therefore well recognized that measuring fatigue damage accumulation is difficult, time-consuming, and in many cases highly variable. Better methods for monitoring the progression of damage are thus needed for asphalt mixtures because of their heterogeneity and inherited variability. The primary objective of this research was to develop a scanning laser system that would detect changes in surface properties for the purposes of monitoring damage and characterizing the fatigue behavior of asphalt mixtures. This technique characterizes the surface state with a defect frequency parameter by rapidly scanning a laser beam along the specimen. Results were found to correlate quite well with data from other traditional mechanical tests (50% reduction in stiffness) and estimated dissipated energy approaches. This laser system is believed to offer many advantages for testing asphalt mixtures as compared with the conventional mechanical systems. The new approach provides the opportunity to quantify the microcrack formation rate and to evaluate the fatigue performance of asphalt mixtures without the need for fixtures on the sample. This system also has the potential of being used in situ for pavement monitoring.

Application of Seismic Energy Dissipation Approach to Curved Continuous Girder Bridge

Under earthquake action there are irregular rotating displacements in the curved girder bridge, and the effective seismic mitigation method for curved bridge need to be systematically studied. The spatial finite element model is established for a curved continuous girder bridge with double-column piers. Energy dissipation dampers including E-steel dampers, viscous dampers, friction pendulum bearings and lead rubber bearings are set in radial and tangent directions of the curve at the positions of active bearings. The seismic mitigation effectiveness and seismic response characteristics of the curved girder bridge are calculated and analyzed with the four energy dissipation approaches under three dimensional ground motion action. The results indicate that the four energy dissipation approaches can all effectively reduce the bending moments and torsional moments at the bottom of piers, and the bending torsion coupling effect of the curved girder bridge is decreased a bit. The difference of internal force for inside and outside piers is reduced after the dampers set for the curved girder bridge with double-column piers. Relatively, the viscous damper approach can further reduce the whole seismic responses of curved continuous girder bridge, and is an excellent seismic mitigation method suitable for curved girder bridge.

Experimental and numerical modelling of wheel–rail contact and wear

In the field of simulation of railroad vehicles, there are many numerical models to estimate the interaction forces between the wheel and rail. The main advantage of these models is that they can be used together with multi-body dynamics software to calculate the motion of a vehicle in real time. However, the result of these contact models is usually post-processed to estimate wear on the profiles and some hypotheses assumed by the contact models may be inadequate for wear analysis. This is the case when considering surface roughness, which is not introduced in the numerical models and makes wear prediction imprecise. In this work an experimental method based on the measurement of ultrasonic reflection is used to solve the contact problem, together with a FASTSIM (simplified theory of rolling contact) algorithm. This technique is suitable to deal with rough surfaces and gives a better approximation of the material behaviour. Wear is estimated by means of the energy dissipation approach (T·gamma). Two different contacts are investigated, using wheel and rail profiles coming from unused and worn specimens. In order to obtain realistic results, special care is taken when locating the specimens to reproduce the same contact that appears between the wheel and the rail in the track.

Oscillations of weakly viscous conducting liquid drops in a strong magnetic field

We analyse small-amplitude oscillations of a weakly viscous electrically conducting liquid drop in a strong uniform DC magnetic field. An asymptotic solution is obtained showing that the magnetic field does not affect the shape eigenmodes, which remain the spherical harmonics as in the non-magnetic case. A strong magnetic field, however, constrains the liquid flow associated with the oscillations and, thus, reduces the oscillation frequencies by increasing effective inertia of the liquid. In such a field, liquid oscillates in a two-dimensional (2D) way as solid columns aligned with the field. Two types of oscillations are possible: longitudinal and transversal to the field. Such oscillations are weakly damped by a strong magnetic field – the stronger the field, the weaker the damping, except for the axisymmetric transversal and inherently 2D modes. The former are overdamped because of being incompatible with the incompressibility constraint, whereas the latter are not affected at all because of being naturally invariant along the field. Since the magnetic damping for all other modes decreases inversely with the square of the field strength, viscous damping may become important in a sufficiently strong magnetic field. The viscous damping is found analytically by a simple energy dissipation approach which is shown for the longitudinal modes to be equivalent to a much more complicated eigenvalue perturbation technique. This study provides a theoretical basis for the development of new measurement methods of surface tension, viscosity and the electrical conductivity of liquid metals using the oscillating drop technique in a strong superimposed DC magnetic field.

Atomistic Simulations of the Load Dependant Friction Force Between Silicon Tip and Diamond Substrate

In this paper, the load dependence on the interfacial friction between a cubic silicon tip and diamond substrate was investigated using molecular dynamics simulations. With the increase of the applied load, the sliding process experiences the states of superlubricity, single slip instability, double slip instability and plastic stage. The transitions from one state to the next one occur at the contact pressure 5.3 GPa, 8.0 GPa and 10.8 GPa, sequentially. In the superlubricity state, both friction and dissipated energy approach zero, independent of the load. However, in the single slip state the friction has a linear relationship with load, while the double slip mode induces decreased frictional force and lower damping. The coupling of the structure and forces in the plastic regime leads to the reduction of friction. These behaviors show good agreement with the recent experimental observations and theoretical predictions.

Application of Shakedown Theory in Characterizing Traditional and Recycled Pavement Base Materials

To facilitate the use of recycled materials in pavement construction, a mechanistic-based approach is required to better characterize pavement base materials. This paper demonstrates the application of the shakedown theory to characterize the behavior of traditional and recycled base materials based on laboratory repeated load triaxial RLT tests and full-scaled accelerated loading tests. A new approach that is based on dissipated energy is proposed to explain different shakedown responses of tested materials under repeated loading. The dissipated energy approach illustrated that there are two responses during RLT tests, namely, stable and unstable responses, which are dependent on the loading levels and type of tested material. It was also observed that the transition from the stable to unstable response represents gradual microstructural adjustments of tested materials to accommodate the applied loading. This gradual transition explains the difficulties in identifying some material responses within the shakedown theory based only on the permanent strain rate criteria. Based on the results of this study, a mechanistic-based design procedure to incorporate various recycled materials into pavement bases is recommended.

Characterization of Fatigue and Healing in Asphalt Binders

Asphalt mixtures have two healing mechanisms: adhesive healing at the asphalt-aggregate interface and cohesive healing within asphalt binders. This study investigates the effects of cohesive healing exclusively, without considering the interaction of aggregates. This study also introduces a methodology of quantifying healing using the dissipated energy approach and the dynamic shear rheometer test with a specifically designed intermittent loading sequence. The ratio of dissipated energy change approach, which is based on the fundamental concept of dissipated energy and has been successfully applied to study hot mix asphalt (HMA) mixture healing, is applied to the binder. By doing so, a healing rate, defined as the rate of dissipated energy recovery per unit of rest time, is used to quantify the healing potential of asphalt binders. The results indicate that binder type, strain level, and temperatures have important impact on healing. It is recommended that the research methods introduced in this study be further applied to asphalt mastics and sand asphalt mixes to study adhesive and cohesive healing in HMA mixtures and provide fatigue-healing information for pavement design.

Modelling of unlubricated oscillating sliding wear of DLC-coatings considering surface topography, oxidation and graphitisation

The improvement of high-performance anti-wear diamond-like carbon-coatings (DLC-coatings) for industrial applications is usually supported by using an oscillating sliding model test. A ball-on-disc setup allows the simulation of accelerated conditions in an unlubricated contact at increased contact pressure. Although the wear behaviour of DLC-coatings has been frequently investigated in literature, wear models for the prediction of the coating's lifetime and for the quantification of wear in the steel counterpart are missing. In this study a unified wear model has been developed based on the dissipated energy approach. This novel model includes evolution equations for the quantitative description of the surface topography of the coated sample, the oxidation of the 100Cr6 steel counterpart as well as the characteristic graphitisation of the DLC-coating. It has been implemented in the Global Incremental Wear Model (GIWM), which accounts for the geometry change during wear and allows a fast wear calculation and model development by simulating all important quantities of the model tests. This GIWM has been validated with experimental results and its predictive capabilities have been demonstrated for different types of DLC-coatings.

Selecting solid lubricant coatings under fretting conditions

Based on the investigation of several bonded solid lubricant coatings under fretting contact, a systemic approach was put forward to help the coating selection for fretting conditions. Some simple techniques, like ball cratering, scratch test and nanoindentation test, can be used to pre-select the coatings, because the fretting endurance of the coatings was found to be closely related to their behaviors in ball cratering and scratch tests. The fretting performance of the candidate coatings was further compared by a dissipated energy approach, where the lifetime of each coating can be fitted by one master curve whatever the contact pressure and the displacement amplitude. The comparison of the master curves for different coatings can help the coating selection. The master curve of a given coating may also be used to predict the coating lifetime only by knowing the initial energy dissipated in the contact. Finally, a straightforward and synthetic evaluation and comparison of the coatings from several aspects can be realized by a polar diagram.

Fretting wear of stainless steels under variable temperature conditions: Introduction of a ‘composite’ wear law

Fretting wear is perceived as a plague in many industrial fields (aeronautics, nuclear engineering, etc.). It is defined as a small displacement amplitude oscillatory motion between two contacting bodies. In this study, Jethete M152 steel was tested against A-286 steel under low pressure gross slip fretting conditions throughout a wide range of constant and variable temperatures from 23°C to 400°C. Friction and wear quantifications using a dissipated energy approach were carried out. Tests performed under constant temperature conditions show tribological discontinuities around 220°C. Above this threshold temperature (Tt) a decrease of the friction coefficient and wear rate is observed, which is related to a significant modification of the interface. At lower temperatures severe adhesive wear dominates whereas at higher ones a third body abrasive process, involving the formation of a compliant glaze layer structure takes place. Various structural analyses including Raman spectroscopy confirm the hypothesis that the glaze layer structure is activated through a tribo-sintering process of oxidized wear particles.Besides, it is shown that the energy wear approach allows the wear kinetics to be determined. However, two different energy wear coefficients were identified depending on the temperature range. This confirms the idea that each wear mechanism is characterized by a specific wear rate. Variable temperature test conditions consisting of repeated sequences at 200°C and 400°C demonstrate a rather high reactivity of the interface regarding the evolution of the wear kinetics. Finally, a ‘composite’ wear law integrating the energy wear coefficient as a function of the temperature is introduced and its stability evaluated.

Application of Elastic–Viscoelastic Correspondence Principle to Determine Fatigue Endurance Limit of Hot-Mix Asphalt

The fatigue endurance limit is one of the properties of hot-mix asphalt (HMA) that govern fatigue behavior of flexible pavements. Some approaches for determining the endurance limit of HMA are empirical in nature, such as the phenomenological approach. This often requires a series of tests at different strain levels and subsequent determination of the relationship between strain and number of repetitions for failure. The mechanics-based dissipated energy approach is more fundamental. However, it fails to take viscoelastic effects into account. Both approaches require considerable amounts of time and resources. This paper presents an alternative approach for determining the fatigue endurance limit of asphalt concrete by means of the elastic–viscoelastic correspondence principle, by separating the effect of viscoelasticity from that of damage development. Three different asphalt concrete mixes, replicates of the National Center for Asphalt Technology (NCAT) test track mixes, were tested for validation of the proposed methodology. Initially the cut and cored samples were tested for dynamic modulus to construct the master curves. With the data, viscoelastic properties were determined by interconversion techniques. In the next stage, fatigue tests were conducted under different strain amplitudes, starting from low to high. Then the strain data were converted to pseudostrain via the elastic–viscoelastic correspondence principle. The endurance limit was determined by identifying the strain level at which a loop between stress and pseudostrain began to develop. Endurance limit values thus determined are comparable to those obtained by flexural tests performed at NCAT. The proposed methodology can contribute to considerable savings in time and resource requirements.

A Dissipated Energy Approach to Fatigue Crack Growth in Ductile Solids and Layered Materials

This paper summarizes recent work on a new theory of fatigue crack growth in ductile solids based on the total plastic energy dissipation per cycle ahead of the crack. The fundamental hypothesis of the theory proposes a unified criterion for crack extension under monotonic and fatigue loading, so that the fatigue crack growth rate is given explicitly in terms of the total plastic dissipation per cycle and the monotonic fracture properties of the material. The total plastic dissipation per cycle is obtained by 2-D elastic-plastic finite element analysis of a stationary crack under constant amplitude loading, for both mode I (C(T)) and general mixed-mode I/II specimen geometries. Both elastic-perfectly plastic and bi-linear kinematic hardening constitutive behaviors are considered, and numerical results for a dimensionless plastic dissipation per cycle are presented over a wide range of relevant mechanical properties and mixed-mode loading conditions. Results are further extended to include fatigue delamination of layered material systems, where either discrete mismatches or a continuous grading of mechanical properties can exist across the interface.

Fretting wear of a TiN PVD coating under variable relative humidity conditions—development of a ‘composite’ wear law

Fretting is defined as a small oscillatory displacement between two contacting bodies. The interface is damaged by debris generation and its ejection from the contact area. The application of hard coatings is an established solution to protect against fretting wear. For this study a TiN hard coating manufactured by a PVD method was selected, and tested against a smooth polycrystalline alumina ball. A fretting test programme was carried out at a frequency of 5 Hz, 100 N normal load, 100 μm displacement amplitude and at five values of relative humidity: 10, 30, 50, 70 and 90% at a temperature of 296 K. The intensity of the wear process is shown to be significantly dependent on the environmental conditions. A dissipated energy approach was employed in this study to quantify the wear rates of the hard coating. The approach gives stable prediction of wear kinetics under constant medium relative humidity. An increase of relative humidity is shown to promote the formation of hydrated structures at the interface and modify the third body rheology. This phenomenon was characterized by the evolution of wear kinetics associated with a significant variation of the corresponding energy wear coefficient. Hence, a ‘composite’ wear law, integrating the energy wear coefficient as a function of relative humidity, is introduced. It permits a prediction of wear under variable relative humidity conditions from 10 to 90% within a single fretting test. The stability of this approach is demonstrated by comparing various variable relative humidity sequences.

Fretting Wear Behavior of Cu–Al Coating on Ti-6Al-4V Substrate under Dry and Wet (Lubricated) Contact Condition

The fretting wear behavior of Cu–Al coating was investigated with and without fatigue load under the dry and wet (lubricated) contact conditions. The Cu–Al coating was plasma deposited on titanium alloy, Ti-6Al-4V. Fretting regime was determined from the shape of fretting hysteresis loop. Fretting regime changed from partial slip to total (gross) slip at ∼15 μm of the applied relative displacement, and this transition point was independent of fatigue loading and contact surface (lubricated versus dry) conditions. Wet contact condition reduced frictional force during cycling, as evidenced by the lower-tangential force. Wear analysis using the accumulated dissipated energy approach did not show any effect of contact surface condition. In other words, the relationship between the accumulated dissipated energy and wear volume showed a linear relationship, and it was independent of loading and contact surface conditions, as well as of the fretting regime. Further, the relationship between the wear depth and accumulated dissipated energy did not show any effect of loading and contact surface conditions, as well as of the fretting regime up to instant when the maximum wear depth was equal to the coating thickness.

Characterization of fretting wear behavior of Cu–Al coating on Ti–6Al–4V substrate

Fretting wear and fretting fatigue are two commonly observed material damages when two contacting bodies with a clamping load are under the oscillatory motion. In this study, fretting wear damage of Cu–Al coating on titanium alloy, Ti–6Al–4V substrate was investigated using the dissipated energy approach. Fretting tests were conducted with either no fatigue load or the maximum fatigue load of 300 MPa and stress ratio of 0.1 on the substrate (specimen). In order to investigate the effect of contact load and contact size, different pad sizes and contact loads were used in the tests. Accumulated dissipated energy versus wear volume data showed a linear relationship regardless of fatigue loading condition on specimen with the smaller pad size. However, two separate linear relationships were observed based on the fatigue loading condition with the larger pad size, such that a relatively more dissipated energy was required for a certain amount of wear with fatigue load on the specimen. The linear relationship between the accumulated dissipated energy and wear volume for both pad sizes extended from partial to gross slip regimes and was not affected by the applied contact load. Further, fretting tests with and without fatigue load resulted in different shapes of fretting loops when the larger pad size was used.

Validation Of Initial and Failure Stiffness Definitions in Flexure Fatigue Test for Hot Mix Asphalt

Abstract Flexural beam fatigue testing of asphalt mixtures has been used for nearly 40 years in the pavement industry. Since the development of the test, the definitions of initial and failure stifnesses have not been verified or validated in any comprehensive study. The main objective of this study is to validate the criteria used to define the initial and the final stiffnesses in flexure fatigue testing. In this study, extensive flexure fatigue tests were performed on five typical dense-graded mixtures and an asphalt rubber gap-graded mixture. An optimization approach was used, in which different intial and failure conditions were assumed. Fatigue models were developed using linear regression curve fitting and the conditions that produced the best fit were selected. Both the phenomenological and the dissipated energy approaches were used. Test results conclusively indicated that the initial stiffness should be defined at cycle number 50. In addition, when a phenomenological approach for fatigue is employed, the fatigue stiffness should be taken at 50% of the initial stiffness.A stiffness degradation model was developed, which provided an independent proof that failue occurs when the stiffness of the beam is reduced to 50% of the initial stiffness. This model represents a basic material propertey at which damage accumulation in the mixture has produced an inability of the mix to resist further damage independent of the mode of loading. In contract to the tensile strain-failure approach, data analysis with the energy approach showed that fatigue failure stiffness, taken at 30% of the initial stiffness, provided identical fatigue energy failure regardless of constant stress or strain mode of loading. The results show that the phenomenological and energy approaches provide different definition of failure and the test should be consistent with the method of analysis used.

Fatigue damage analysis in asphalt concrete mixtures using the dissipated energy approach

An asphalt concrete damage–energy fatigue approach based on the concept of change in dissipated energy is presented in this paper. The damage–energy based fatigue approach is simple and based on a sound theoretical background. The central concept of the energy approach is the energy fatigue curve, which is based on two key elements, namely the plateau value (PV) and the number of load cycles to true failure (Ntf). The plateau value represents the constant value of the percentage of dissipated energy that produces damage to the material under cyclic loading. Failure is defined as the number of load cycles at which this percentage of dissipated energy begins to increase rapidly, indicating instability. Flexural fatigue testing was used to test hundreds of asphalt concrete beams, mainly under controlled-strain testing conditions. It was found that PV is highly dependent on the initial loading conditions, stress, strain, and dissipated energy. As a result, it can be used conveniently in pavement design. The number of load cycles to 50% reduction in initial stiffness was found to be highly correlated with the new failure point (Ntf). Using the dissipated energy concepts in fatigue analysis makes it possible to account for damage accumulation in a straightforward manner.Key words: fatigue of asphalt concrete, dissipated energy, damage, energy ratio.

A Dissipated Energy Approach to Fatigue Evaluation

A Dissipated Energy Approach to Fatigue Evaluation

Plastic dissipation in mixed-mode fatigue crack growth along plastically mismatched interfaces

A new theory of fatigue crack growth in ductile solids has recently been proposed based on the total plastic energy dissipation per cycle ahead of the crack. This and previous energy based approaches in the literature suggest that the total plastic dissipation per cycle can be closely correlated with fatigue crack growth rates under mode I loading. In a recent paper, the authors have extended the dissipated energy approach to the case of fatigue crack growth in a homogeneous material under sustained mixed-mode loading conditions. The goal of the current study is to further extend the approach to mixed-mode fatigue delamination of ductile interfaces in layered materials. Attention is restricted to material combinations with identical elastic properties, but with mismatches in plastic properties (both yield strength and hardening modulus) across the interface. Such systems can occur in brazing, soldering, welding, and a variety of layered manufacturing applications, where high-temperature material deposition can result in a mismatch in mechanical properties between the deposited material and the substrate. In this study, the total plastic dissipation per cycle is obtained through plane strain elastic–plastic finite element analysis of a stationary crack in a general layered specimen geometry under constant amplitude, mixed-mode loading. Numerical results for a dimensionless plastic dissipation per cycle are presented over the full range of relevant material combinations and mixed-mode loading conditions. Results suggest that while applied mode-mix ratio is the dominant parameter, mismatches in yield strength and hardening modulus can have a significant effect on the total plastic dissipation per cycle, which is dominated by the weaker/softer material.

Fretting wear of Ti(CxNy) PVD coatings under variable environmental conditions

Fretting wear as a specific type of degradation is defined as an oscillatory motion at small amplitude between two nominally stationary solid bodies in mutual contact. Under external stresses, the interface is being damaged by debris generation and its successive ejections outside the contact area. A potential protection against fretting damage by means of hard coatings is being offered by different surface engineering techniques. For this study, TiC, TiN, and TiCN hard coatings manufactured by a physical vapour deposition method have been selected and tested against smooth polycrystalline alumina ball. A fretting test programme has been carried out at the frequency of 5 Hz, 100 N normal load, 100 μm displacement amplitude, and at three values of a relative humidity (RH): 10, 50, and 90 per cent at 295-298 K temperature. It turned out that the intensity of wear process was depending not only on loading conditions but also on environmental ones. A significant impact of RH on wear rate and friction behaviour of the coatings under investigation has been observed. Two different damage mechanisms have been identified and related to the phenomena of debris oxidation and debris adhesion to the counterbody surface. In the latter case, the debris deposited onto the surface of the alumina ball lead to a change of stress distribution at the interface and as a result to accelerated wear. In this work, experiments with variable RH increasing from 10 to 90 per cent within a single fretting test have been completed. It follows from these experiments that there exists an intermediate value of the RH at which the friction coefficient changes rapidly. Finally, a dissipated energy approach has been applied in the work to quantify and compare fretting wear rates of different hard coatings.