Mixed-mode Model Research Articles

Modelling shattered rim cracking in railroad wheels

Shattered rim cracking, propagation of a subsurface crack parallel to the tread surface, is one of the dominant railroad wheel failure types observed in North America. This crack initiation and propagation life depends on several factors, such as wheel rim thickness, wheel load, residual stresses in the rim, and the size and location of material defects in the rim. This article investigates the effect of the above-mentioned parameters on shattered rim cracking, using finite element analysis and fracture mechanics. This cracking is modelled using a three-dimensional, multiresolution, elastic–plastic finite element model of a railroad wheel. Material defects are modelled as mathematically sharp cracks. Rolling contact loading is simulated by applying the wheel load on the tread surface over a Hertzian contact area. The equivalent stress intensity factor ranges at the subsurface crack tips are estimated using uni-modal stress intensity factors obtained from the finite element analysis and a mixed-mode crack growth model. The residual stress and wheel wear effects are also included in modelling shattered rim cracking. The analysis results show that the sensitive depth below the tread surface for shattered rim cracking ranges from 19.05 to 22.23 mm, which is in good agreement with field observations. The relationship of the equivalent stress intensity factor (Δ K eq) at the crack tip to the load magnitude is observed to be approximately linear. The analysis results show that the equivalent stress intensity factor (Δ K eq) at the crack tip depends significantly on the residual stress state in the wheel. Consideration of as-manufactured residual stresses decreases the Δ K eq at the crack tip by about 40 per cent compared to that of no residual stress state, whereas consideration of service-induced residual stresses increases the Δ K eq at the crack tip by about 50 per cent compared to that of as-manufactured residual stress state. In summary, the methodology developed in this article can help to predict whether a shattered rim crack will propagate for a given set of parameters, such as load magnitude, rim thickness, crack size, crack location, and residual stress state.

A coupled mixed-mode delamination model for laminated composites

Cohesive elements have now become commonplace in many commercial finite element codes. Their use in impact and crash and other complex composite design problems requires the development of more advanced cohesive element formulations capable of predicting mixed-mode behavior during a complex loading. A cohesive zone model is developed for the simulation of delaminations in laminated composites under mixed-mode loadings, based on a coupling between the normal and tangential components of the relative displacement across an interlaminar interface. Featuring a unique characterization of degraded states, this coupling enables a simultaneous loss of loading capacity of the interface in normal and tangential directions, once the criteria on delamination growth are satisfied. Moreover, the variation of mode participation during the delamination process is effectively considered. A comparison between numerical simulations and experimental data on typical delamination tests shows the robustness and the potential of the model.

Modeling of soft impingement effect during solid-state partitioning phase transformations in binary alloys

The soft impingement effect at the later stage of partitioning phase transformations has been modeled both for the diffusion-controlled growth model and for the mixed-mode model. Instead of the linear and exponential approximations for the concentration gradient in front of the interface used in the past, a general polynomial method of dealing with the diffusion field is proposed. The linear and exponential diffusion field approximations are two specific cases of the polynomial diffusion field approximation. The effect of soft impingement on the overall partitioning phase transformation is only related to the degree of the super-saturation in case of the diffusion-controlled growth model, while it is determined by both the growth mode and the degree of super-saturation in case of the mixed-mode model.

A Mixed-Mode Combustion Model for Large-Eddy Simulation of Diesel Engines

Present technologies of diesel engine combustion involve various operating conditions that can lead to a broad spectrum of combustion regimes. Existing combustion models for diesel engines usually lack universality across combustion regimes. In this study, a mixed-mode combustion model was developed to cover the major regimes pertaining to diesel engine combustion. The model uses kinetically controlled, quasi-steady homogeneous, quasi-steady flamelet, and partially premixed combustion modes. The combustion regime is identified locally by two combustion indices based on the local chemical and mixing conditions. The combustion model takes advantage of mixing details provided by large-eddy simulation. The model was tested over a wide range of engine conditions including conventional diesel-type and low-temperature combustion operating conditions. The model results compared well with experimental data and exhibited strength in both universality and computational efficiency.

Application of the cyclic phase transformation concept for investigating growth kinetics of solid-state partitioning phase transformations

A heat treatment involving cyclic partial phase transformations has been analyzed to determining growth kinetics of the austenite to ferrite phase transformation and vice versa more accurately. The mixed-mode model and the diffusion-controlled phase transformation model, including the soft impingement effects at the later stage of phase transformation, are reformulated for the cyclic austenite to ferrite and ferrite to austenite transformation. A new growth mode parameter H is defined for the mixed-mode model. It shows that not all partitioning phase transformations starts as pure interface-controlled growth but all of them shift gradually towards pure diffusion control when thermodynamic equilibrium is approached. The diffusion-controlled model predicts that the ferrite to austenite transformation should be faster than the austenite to ferrite, while the simulation of the mixed-mode model shows that the transformation rate ratio is a function of the ratio of interface mobility.

Mixed-mode-based admission control in WLAN

A mixed-mode (model and measurement)-based admission control algorithm was proposed concerning that IEEE 802.11e EDCA cannot offer quantitative QoS.States transition Markov models of back-off instance were proposed,the analytical expression of network performance indicators could be obtained through Beizer reduction rules,and the achievable throughputs of the new arrived flows were predicted according to measured channel states.Finally admission control algorithm based on throughput was proposed.This scheme shows a good protection of admitted flows and admits more flows,while increasing the throughput of the network.

Achieving Best Practice Manufacturing Involving Tacit Knowledge through the Cautious Use of Mixed-mode Modelling

In the real world, ‘optimal’ solutions for many production process problems do not exist. In such circumstances, ‘best practice’ is the realistic outcome for which practitioners aim. The reasons for this stem from many causes, including that data associated with production processes are often corrupted and/or missing. These types of processes usually rely heavily on the subjective input of the process workers on the shop floor (tacit knowledge). This paper outlines how the use of mixed-mode modelling has been utilised to help solve these types of problems. The industry examples used in the paper incorporate the concept of Communities of Practice (CoPs) in the mixed-mode models that are developed as a means of capturing tacit knowledge and incorporating it into the solution process. Additionally, CoPs need to sit comfortably within the culture and values of the organisation and employee groups, and must be clearly owned and facilitated by the community of workers whose knowledge is to be shared. Finally, CoPs should be presented as opportunities to share, compare, and learn so that a ‘craft’ is not lost or diminished.

Mai i te Whenua ki te Rangi - Transferring Māori pedagogical practices into cyberspace

Abstract E-Learning has become the norm in many of our tertiary institutes in Aotearoa New Zealand. The digital age is upon us and as agents of change in a Māori tertiary environment, we are constantly having to keep abreast of new and innovative ways of teaching and learning. Te Iti Rearea, Bachelor of Teaching and Learning (0-8) Early Years Māori Medium degree at Te Whare Wānanga ō Awanuiārangi has recently made the move from the conventional face to face model of teaching and learning to the mixed mode model. E-Learning is one of the modes of delivery for this programme. The degree is a Māori medium degree and ako or the Māori preferred reciprocal pedagogy underpins the programme. The transfer of Māori pedagogical practices from the conventional face to face model to the e-Learning environment can seem like a mammoth task, but is it? This paper outlines some of the key indicators for the successful transfer of Māori pedagogical practices from conventional to the e-Learning environment from recent studies and projects completed by the author.

A Systematic Development Methodology for Mixed-Mode Behavioral Models of In-Vehicle Embedded Electronic Systems

The rising demands for safety, power-weight reduction, and comfort make the in-vehicle network of embedded electronic systems very complex. In particular system reliability is essential, especially because of the safety requirements. Test and verification of the entire in-vehicle network by means of behavioral simulations are each time more widely adopted. To this aim, behavioral models that faithfully represent the behavior of mixed-mode-embedded systems are essential for achieving reliable simulation results. This paper presents a systematic development methodology for mixed-mode behavioral models of in-vehicle-embedded systems. The methodology allows achieving accurate models, which provide reliable system simulations. The model development methodology is described and the results of the methodology applied to two case studies are presented: (1) the mixed-mode behavioral model of a generic Flexray physical layer transceiver and (2) the mixed-mode behavioral model of a CAN bus transceiver-integrated circuit. The simulation results show that behavioral simulations are much faster than transistor level simulations. Moreover, behavioral simulations are flexible, which allows quickly changing and verifying the communication network topology if compared with hardware prototypes.

MODELING OF PARTICLE SIZE DISTRIBUTION (PSD) DURING THE AGEING PROCESS: A MODIFIED KWN MODEL

During the process of precipitation hardening, the phase decompositions in supersaturated solid solution (SSS) are often initiated by nucleation, then proceed to particle growth and eventually ended by Ostwald coarsening. To produce a model that is valid over the full range of transformation, the competing processes of nucleation, growth and coarsening cannot be considered in isolation. A powerful method for dealing with concomitant nucleation, growth and coarsening has been developed by Kampmann and Wagner. In the present work, the standard Kampmann and Wagner numerical model (KWN model) has been extended and modified to determine the dynamics of particle size distribution (PSD) as well as the microstructure evolution. In the present model, the newly nucleated particles are added to the corresponding size classes using the Trapezoidal shape assumption in order to eliminate the problem of discontinuity. During the growth and coarsening, since phase separations start as an interface-controlled transformation and gradually shift towards diffusion control, the mixed-mode (or co-controlled) model, therefore, is used in the present work instead of the diffusion controlled rate used in the standard KWN. Finally, the model is applied to aluminium alloys under both isothermal and non-isothermal heat treatment conditions.

Mixed-Mode Cohesive Damage Model Applied to the Simulation of the Mechanical Behaviour of Laminated Composite Adhesive Joints

A study of the mechanical behaviour of laminated composite adhesive joints is presented in this paper. The study consists of both numerical simulations and experimental tests. It concentrates on single lap-shear joints made of carbon–epoxy laminated composites and an epoxy adhesive. The main objective is to verify the adequacy of cohesive damage models for the strength prediction of bonded joints. These models are attractive in modelling fracture problems since they do not require the definition of an initial crack and they model damage propagation without any user intervention. A mixed-mode cohesive damage model is used to simulate damage onset and growth in the adhesive layer. The model is an extension of pure mode (I and II) trapezoidal cohesive damage models. The trapezoidal shape in the constitutive law is more valid when ductile adhesives are used. The mixed-mode model requires a complete characterization of the cohesive parameters in pure modes, determined with an inverse method. Tensile tests are performed for joints with different overlap lengths. It is shown that the numerical simulations represent with a reasonable accuracy the mechanical behaviour of the joints tested.

Rate effects for mixed-mode fracture of plastically-deforming, adhesively-bonded structures

Mixed-mode fracture of an adhesively-bonded structure made from a commercial adhesive and a dual-phase steel has been studied under different rates. Since mixed-mode fracture occurs along the interface between the steel and the adhesive, the cohesive parameters for the interface were required. The mode-II interfacial properties were deduced in earlier work. In this paper the mode-I interfacial toughness and the mode-I interfacial strength were determined at different rates. The mode-I interfacial strength was not affected by rate up to crack velocities at levels associated with impact conditions, and was essentially identical to the cohesive strength appropriate for crack growth within the adhesive layer. The mode-I toughness was reduced by about 40% when the crack propagated along the interface rather than within the adhesive. Furthermore, transitions to a brittle mode of failure occurred in a stochastic fashion, and were associated with a drop in interfacial toughness by a factor of about five. The mode-I interfacial parameters were combined with the previously-determined mode-II interfacial parameters within a cohesive-zone model to analyze the mixed-mode fracture of the joints which exhibited both quasi-static and unstable fracture. The mixed-mode model and the associated cohesive parameters for both quasi-static and unstable crack propagation provide bounds for predicting the behavior of the bonded joints under various rates of loading, up to the impact conditions that could be appropriate for automotive design.

Application of the maximum driving force concept for solid-state partitioning phase transformations in multi-component systems

A mixed-mode model is defined for solid-state phase transformation in multi-component systems. In contrast to diffusion-controlled phase transformation models, the mixed-mode nature of the presented transformation model takes the effect of a finite interface mobility into account over the entire temperature range of the transformation. In the model the maximum driving force concept is applied to determine the composition at the interface of the newly formed phase. This phase forms with the composition that gives the largest gain in free energy, i.e., the largest driving force. The model makes no a priori assumptions about the partitioning behaviour of any of the alloy components. As shown by example calculations on the austenite to ferrite transformation in an Fe–C–Mn steel, the model predicts a transition from partitioning to negligible partitioning of the substitutionally dissolved alloying elements during cooling.

Cohesive mixed mode fracture modelling and experiments

A nonlinear mixed mode model originally developed by Wernersson [Wernersson H. Fracture characterization of wood adhesive joints. Report TVSM-1006, Lund University, Division of Structural Mechanics; 1994], based on nonlinear fracture mechanics, is discussed and applied to model interfacial cracking in a steel–concrete interface. The model is based on the principles of Hillerborgs fictitious crack model, however, the Mode I softening description is modified taking into account the influence of shear. The model couples normal and shear stresses for a given combination of Mode I and II fracture. An experimental set-up for the assessment of mixed mode interfacial fracture properties is presented, applying a bi-material specimen, half steel and half concrete, with an inclined interface and under uniaxial load. Loading the inclined steel–concrete interface under different angles produces load–crack opening curves, which may be interpreted using the nonlinear mixed mode model. The interpretation of test results is carried out in a two step inverse analysis applying numerical optimization tools. It is demonstrated how to perform the inverse analysis, which couples the assumed individual experimental load–crack opening curves. The individual load–crack opening curves are obtained under different combinations of normal and shear stresses. Reliable results are obtained in pure Mode I, whereas experimental data for small mixed mode angles are used to extrapolate the pure Mode II curve.

A mixed-mode building energy model for performance evaluation and diagnosis of existing buildings

Building level energy models are important to provide accurate energy consumption prediction for building performance diagnosis at building level as well as energy efficiency assessment of retrofitting alternatives for building performance upgrading. However, it is a great challenge to establish building energy models of existing buildings for long-term energy performance prediction only using short-term monitoring operation data. In this study, a mixed-mode building energy model is proposed to describe building system for thermal performance prediction at the building level. The model includes two parts. One part is the simplified energy models (3R2C) of building envelopes. The parameters of these simplified models are determined by comparing the frequency characteristics of those simplified models and their theoretical frequency characteristics based on the easily available detailed physical properties of exterior walls and roof. The other part is the simplified 2R2C model for building internal mass, whose detailed physical properties are very difficult to obtain. The parameters of the building internal mass model are optimised using short-term monitored operation data. A genetic algorithm estimator is developed to optimise these parameters. The parameter optimisation of the simplified building internal mass model (2R2C) and the mixed-mode building energy model are validated in a high rising commercial office building under various weather conditions. An application of this model for performance evaluation of alternative control strategies is illustrated briefly.

Determining best practice production in an aluminium smelter involving sub-processes based substantially on tacit knowledge: an application of Communities of Practice

This paper considers the difficulties associated with a production process that contains a sub-process that is not fully understood and for which data for many parameters are only able to be approximately obtained. The aluminium smelting industry epitomizes such a situation. Here, the critical sub-process that exemplifies these difficulties is the actual heart of the smelter, the electrolytic processing of alumina. This sub-process of aluminium production is at best ‘fuzzy’ and relies on the smelter operators to use their experience and tacit knowledge on a day-to-day basis, that is, the sub-process involves ‘alchemy’. In this paper, this is referred to as the tacit knowledge problem. The impact of such sub-processes on production is significant and the development of a methodology that will lead to a reduced reliance on uncertain alchemy associated with them, highly beneficial. The role of Communities of Practice in finding a solution to the tacit knowledge problem is discussed together with its integration into a mixed-mode model for the determination of best practice production for the smelter.

A mixed-mode model for partitioning phase transformations

A mixed-mode model for the interface velocity during partitioning phase transformations [J. Sietsma, S. van der Zwaag, Acta Mater. 52 (2004) 4143–4152] is reformulated and rigorously validated. Comparison with a numerical treatment shows that the model gives a near-exact description of the growth kinetics. In addition, the model provides information on the concentration profiles of the partitioning element. The mixed-mode growth model can be combined with a range of different microstructure models. As an example a combination with a Johnson–Mehl–Avrami extended volume model is shown.

The mechanism of the effects of the upwelling mean on the ENSO event mature phase locking

The mechanism of the effects of the upwelling mean on the ENSO event mature phase locking is examined by using a mixed-mode model. The results show that the positive feedback process of the effects of the seasonal variation of the upwelling mean on the Kelvin wave is the mechanism of the locking of the event mature phase to the end of the calendar year. The memory of the Rossby waves for the sign-shifting of the sea surface temperature anomaly from positive to negative 6 months before the cold peak time is the other mechanism of the locking of the La Nina event mature phase to the end of the calendar year. The results here are different from previous ones which suggest that the balance between cold and warm trends of sea surface temperature anomaly is the mechanism involved. The cold trend is caused by the upwelling Kelvin wave from upwelling Rossby wave reflected at the western boundary, excited by the westerly anomaly stress over the central Pacific and amplified by the seasonal variation of the coupled strength in its way propagating westward. The warm trend is caused by the Kelvin wave forced by the western wind stress over the middle and eastern equatorial Pacific. The cause of the differences is due to the opposite phase of the seasonal variation of the upwelling mean to that in the observation and an improper parameterization scheme for the effects of the seasonal variation of the upwelling mean on the ENSO cycle in previous studies.

The Effect of the Impactor Diameter and Boundary Conditions on Low Velocity Impact Composites Behaviour

The aim of present work is to study the influence of the impactor diameter and boundary conditions on low velocity impact on carbon-fibre-reinforced epoxy laminates. Experimental tests were performed on [04,904]s laminates, using a drop weight-testing machine. Circular plates were tested under low velocity impacts for two diameters of the hemispherical impactor, 12.7 mm and 20 mm, and considering similar impact energies, 2.6 J for the first impactor and 3 J for the second one. Rectangular and square plates were analysed under low velocity impacts with different boundary conditions. The impacted plates were inspected by X-radiography. Numerical simulations were also performed considering interface finite elements compatible with three-dimensional solid elements including a cohesive mixed-mode damage model, which allows to model delamination between layers. The impact tests showed that both the impactor’s diameter and boundary conditions have influence on the delaminated area. Good agreement between experimental and numerical analysis for shape, orientation and size of damage was obtained.

Modelling of the β → α + β transformation in a metastable β Ti alloy based on the growth kinetics and the morphology of the α plates

Abstract The kinetics of the isothermal β → α + β transformation in a metastable β titanium alloy has been studied by dilatometry. Based on thermodynamic aspects, the volume diffusion of Mo in the titanium matrix ahead of the interface, the interface mobility, and the morphology of the primary α plates, a transformation model is developed, which incorporates mixed-mode behaviour of the transformation in the initial stage. Fraction curves are calculated based on the simulated growth of a typical α plate within the β phase having a volume determined from the nucleus density. For comparison, fraction curves are calculated using a three-dimensional model of the β grain in which a number of plates are simulated to grow with purely diffusion-controlled kinetics. It is shown that the calculated growth rate with the mixed-mode transformation model gives a better representation of the growth rate at the start of the transformation than the purely diffusion-controlled model.