etd@IISc Community:
http://hdl.handle.net/2005/801
2017-10-13T19:42:07ZPartial Slip Contacts in Linear Viscoelasticity
http://hdl.handle.net/2005/2698
Title: Partial Slip Contacts in Linear Viscoelasticity
Authors: Dayalan, Satish Kumar
Abstract: This work analyzes partial slip contact problems in the theory of linear viscoelasticity using both the semi-analytical method and nite element method. Such problems arise in metal-polymer contacts in orthopedic implants and similar applications. The boundary conditions of such problems are inherently mixed and vary with time, thus restricting the use of classical correspondence principle, which have been the basic approach for most of the solved problems in viscoelasticity. In the present semi-analytical approach, the governing equations for the vis-coelastic partial-slip contact are formulated as a pair of coupled Singular Integral Equations (SIEs) for a pin-plate geometry using the viscoelastic analogues of Green's functions. The formulation is entirely in the time-domain, avoiding Laplace transforms. Both Coulomb and hysteretic e ects are considered, and arbitrary load histories, including the bidirectional pin loads and remote plate stresses, are allowed. Moreover, the contact patch is allowed to advance and recede with no restrictions. The presence of viscoelastic behavior necessitates the application of the stick zone boundary condition in convolved form, and also introduces additional convolved gap terms in the governing equations, which are not present in the elastic case. Transient, as well as steady-state contact tractions, are obtained under load-hold, unload-hold, unload-reload, cyclic bidirectional (fretting) and remote plate loading for a three-element delayed elastic solid. A wide range of loads, loading rates, friction coeficients and the conforming nature of the contact are considered. The contact size, stick-zone size, indenter approach, maximum pressure, Coulomb energy dissipation are tracked during fretting. The edge-of-contact stresses and the subsurface stresses for the viscoelastic plate due to the contact tractions are determined by solving an equivalent traction boundary value problem.
It is found that the viscoelastic fretting contact tractions for materials with delayed elastic nature shakedown just like their elastic counterparts. However, the number of cycles to attain shakedown states is strongly dependent on the ratio of the load cycle time to the relaxation time constant of the viscoelastic material. In monotonic load-hold case, the viscoelastic steady-state tractions agree well with the tractions from an equivalent elastic analysis using the shear modulus at infinite time. Whereas, the viscoelastic fretting tractions in shakedown differ considerably from their elastic counterparts. This is due to the fact that the contact patch does not increase monotonically in fretting-type(cyclic) loading. Hence, an approximate elastic analysis misleads to an incorrect edge-of-contact stresses. During fretting, the edge-of-contact hoop stress also shakedown and reaches its peak value at the trailing edge-of-contact when the horizontal pin load reaches its maximum.
Moreover, the peak tensile of the edge-of-contact hoop stress increases with the increase in the Coulomb friction coefficient. In cyclic loading, Coulomb dissipation in a cycle at steady-state is almost independent of the rate at which the load is cycled. However, the viscous energy dissipated in a cycle is a strong function of the ratio of the load cycle time to the relaxation time constant. The steady-state cyclic hysteretic energy dissipation typically dominates the cyclic Coulomb dissipation, with a more pronounced difference at slower load cycling. However, despite this, it is essential to model an accurate viscoelastic fretting contacts including the effects of both viscous and Coulomb friction dissipation to obtain accurate contact stresses.
A 12-element generalized Maxwell solid with long time scales representing a well characterized viscoelastic material like PMMA is also studied. The material chosen is of slowly relaxing nature and the ratio of the instantaneous shear modulus(G0) to the modulus at the infinite time(G1) is almost equal to 1000. In such cases, the material is effectively always in a transient state, with no steady edge-of-contact. As a consequence, the location of the peak hoop stress keeps on shifting when the load cycle is repeated. Interestingly, the rate at which the viscoelastic material relaxes affects the contact tractions. It is observed that the rapidly relaxing materials show qualitatively different tractions in the partial slip, with local traction spikes close to the edges-of-contact and concomitant high-stress gradients.
On the other hand, finite element method is also used to analyze the partial slip viscoelastic contacts. In FEA, the pin-plate geometry is modeled using a custom mesh maker, where a 2D-continuum plane strain element is used for the plate and rigid element for the pin. The technique uses 'ABAQUS Standard' solver to solve the contact problem. Finite element analysis for a wide range of loads comparable with the SIE technique is performed. The tractions and contact sizes for various load cases such as unload-reload, fretting-type cyclic loads from both SIE and FEA agrees well. In certain conditions, there exist multiple contact arcs or stick zones that are currently difficult to solve with SIE's. However, such problems are treated using FEA and one such problem is illustrated.2017-10-04T18:30:00ZExperimental Studies on The Mechanical Behaviour of Cohesive Frictional Granular Materials
http://hdl.handle.net/2005/2680
Title: Experimental Studies on The Mechanical Behaviour of Cohesive Frictional Granular Materials
Authors: Kandasami, Ramesh Kannan
Abstract: Thss thesis presents the results of an experimental programme on the static mono-tonic response of cohesive-frictional granular materials. The purpose of this experimental programme was to gain insight into the mechanical behaviour of uncemented sands, and sands with small percentages of cementation. With this objective in sight, the research involved understanding and delineating the e ects of four variables: the intermediate principal stress, stress inclination, cohesion (or cementation), and particle morphology. The hollow cylinder torsion (HCT) apparatus, which allows control over both the magnitude and direction of principal stresses, was used in this study to carry out a series of elemental tests on the model materials. The test results were analysed in a plasticity theory based framework of critical state soil mechanics.
Drained and undrained HCT tests were conducted on a model angular sand to understand the combined influence of intermediate principal stress ratio (b) and principal stress inclination ( ). Sand specimens were reconstituted to a given density and confining pressure, and were sheared to large strains towards a critical state. The stresses at the critical state with varying `b' were mapped on an octahedral plane to obtain a critical state locus. The shape of this locus closely resembles a curved triangle. Also these specimens showed increased non-coaxiality between the stress and strain increment directions at lower strains. This non-coaxiality decreased significantly, and the response at the critical state was by and large coaxial. The effect of `b' and ` ' on the flow potential, phase transformation, and critical state was also investigated. At phase transformation, ` ' plays a more dominant role in determining the flow potential than `b'. The shape and size of the critical state locus remained the same immaterial of the drainage conditions.
Next, small amounts of cohesion (using ordinary Portland cement) was added to this sand ensemble to study the mechanical behaviour of weakly cemented sands. The peak in the stress strain curve was used to signal the breakdown of cohesion further leading to a complete destructuring of the sand at the critical state. The response of the cemented sand changes from brittle to ductile with increase in confining pressure, while reverses with increase in density and `b'. Stress-dilatancy response for the weakly cemented materials shows the non coincidence of peak stress ratio and maximum value of dilation unlike purely frictional materials. This mismatch in peak stress ratio and maximum dilation diminishes with increase in confining pressure. The peak stress (cemented structured sand) locus and the critical state (destructured) locus were constructed on the octahedral plane from these HCT tests. The critical state locus of the cemented sand when it is completely destructured almost coincides with the critical state locus of the clean sand. Using this experimental data set, some important stress-dilatancy relationships (like Zhang and Salgado) and failure criteria (Lade's isotropic single hardening failure criteria and SMP failure criteria) were benchmarked and their prediction capabilities of such models were discussed in detail.
The effect of particle morphology was also investigated in this testing programme. Rounded glass ballotini and angular quartzitic sand which occupy two extreme shapes were selected, and a series of HCT tests at different `b' values were con-ducted. A larger sized CS locus was obtained for angular particles and it encompassed the critical state locus of the spherical glass ballotini. Spherical particles exhibit a predominantly dilative behaviour, however present a lower strength at the critical state. The mobilization of strength as a result of rearrangement of angular particles and the consequent interlocking is higher. Even with contractive behaviour which is reflected in the higher values of critical state friction angle and the larger size of the yield locus for sand.
Finally, a series of unconfined compression tests were performed to understand if there exists a scale separation in cohesive frictional materials. Specimens were reconstituted to a range of sizes while maintaining a constant aspect ratio and density. As the specimen size increased, the peak strength also increases, counter to an idea of a generalized continuum for all model systems. The observed secondary length scale (in addition to the continuum length scale) is obverse to the one observed in quasi-brittle materials such as concrete, rock. In order to ascertain the reason behind this phenomenon, a series of tomography studies were carried out on these contact-bound ensembles. The presence of cohesion between the grains brings about an \entanglement" between the grains, which contributes to increase in strength, with increase in the size of the sample. This in e ect bringing forth a second length scale that controls the behaviour of these cohesive frictional granular materials.
This experimental data set provides quantification of various aspects of the me-chanical response of both cemented and uncemented granular materials under myriad stress conditions. This data set is also extremely useful in developing and bench-marking constitutive models and simulations.2017-09-25T18:30:00ZExperiments And Analysis on Wood Gasification in an Open Top Downdraft Gasifier
http://hdl.handle.net/2005/2685
Title: Experiments And Analysis on Wood Gasification in an Open Top Downdraft Gasifier
Authors: Mahapatra, Sadhan
Abstract: The thesis, through experimental and numerical investigations reports on the work related to packed bed reactors in co-current configuration for biomass gasification. This study has extensively focused on the gasification operating regimes and addressing the issues of presence of tar, an undesirable component for engine application.
Systematically, the influence of fuel properties on the gasification process has been studied using single particle analysis and also in packed bed reactors. Studies related to the effect of fuel properties - size, surface area volume ratio and density on the reactor performance are addressed. The influence of these parameters on the propagation rate which indirectly influences the residence time, tar generation, gas compositions is explicitly elucidated. Most of the reported work in literature primarily focuses on counter-current configurations and analysis on propagation flame front/ignition mass flux and temperature profiles mostly under the combustion regime. In this work, flame propagation front movement, bed movement and effective movement for a co-current packed bed reactor of different reactor capacities and a generalized approach towards establishing ‘effective propagation rate’ has been proposed. The work also reports on the importance of particle size and sharing of air from the top and through nozzles on tar generation in the open top down draft reactor configuration.
Firstly, pyrolysis, an important component of the thermochemical conversion process has been studied using the flaming time for different biomass samples having varying size, shape and density. The elaborate experiments on the single particle study provides an insight into the reasons for high tar generation for wood flakes/coconut shells and also identifies the importance of the fuel particle geometry related to surface area and volume ratio. Effect of density by comparing the flaming rate of wood flakes and coconut shells with the wood sphere for an equivalent diameter is highlighted. It is observed that the tar level in the raw gas is about 80% higher in the case of wood flakes and similar values for coconut shells compared with wood pieces. The analysis suggests that the time for pyrolysis is lower with a higher surface area particle and is subjected to nearly fast pyrolysis process resulting in higher tar fraction with low char yield.
Similarly, time for pyrolysis increases with density as observed from the experimental measurements by using coconut shells and wood flakes and concludes the influence on the performance of packed bed reactors. Studies on co-current reactor under various operating conditions from closed top reactor to open top reburn configuration suggests improved residence time reduces tar generation. This study establishes, increased residence time with staged air flow has a better control on residence time and yields lower tar in the raw gas.
Studies on the influence of air mass flux on the propagation rate, peak temperature, and gas quality, establishes the need to consider bed movement in the case of co-current packed bed reactor. It is also observed that flame front propagation rate initially increases as the air mass flux is increased, reaches a peak and subsequently decreases. With increase in air mass flux, fuel consumption increases and thereby the bed movement. The importance of bed movement and its effect on the propagation front movement has been established. To account for variation in the fuel density, normalized propagation rate or the ignition mass flux is a better way to present the result. The peak flame front propagation rates are 0.089 mm/s for 10 % moist wood at an air mas flux of 0.130 kg/m2-s and while 0.095 mm/s for bone-dry wood at an air mass flux of 0.134 kg/m2-s. These peak propagation rates occur with the air mass flux in the range of 0.130 to 0.134 kg/m2-s. The present results compare well with those available in the literature on the effective propagation rate with the variation of air mass flux, and deviations are linked to fuel properties. The propagation rate correlates with mass flux as ̇ . during the increasing regime of the front movement. The extinction of flame propagation or the front receding has been established both experimentally supported from the model analysis and is found to be at an air mass flux of 0.235 kg/m2-s. The volume fraction of various gaseous species at the reactor exits obtained from the experiment is 14.89±0.28 % CO2, 15.75±0.43 % CO and 11.09±1.99 % H2 respectively with the balance being CH4 and N2.
The model analysis using an in-house program developed for packed bed reactor provide a comprehensive understanding with respect to the performance of packed bed reactor under gasification conditions. The model addresses the dependence on air mass flux on gas composition and propagation rate and is used to validate the experimental results.
Based on the energy balance in the reaction front, the analysis clearly identifies the reasons for stable propagation front and receding front in a co-current reactor. From the experiments and modelling studies, it is evident that turn-down ratio of a downdraft gasification system is scientifically established. Both the experimental and the numerical studies presented in the current work establishes that the physical properties of the fuel have an impact on the performance of the co-current reactor and for the first time, the importance of bed movement on the propagation rate is identified.2017-09-25T18:30:00ZEffect of Cyclic Strain Path And Vibration Cycles on Shear Modulus And Damping of Sand
http://hdl.handle.net/2005/2675
Title: Effect of Cyclic Strain Path And Vibration Cycles on Shear Modulus And Damping of Sand
Authors: Cherian, Achu Catherine
Abstract: The soil strata is often subjected to various kinds of vibrations such as that caused by earthquakes, water waves, traffic loads, wind power plants, construction related equipments, pile driving and vibratory machines. The strains induced in a soil mass due to the vibrations generated by these different sources often lie in a range of 0.0001% - 0.1%. The estimation of the shear modulus (G) and damping (D) of soils in this strain range becomes an important aspect for performing the analysis and design of various geotechnical structures subjected to different kinds of vibrations. Strain amplitude, effective confining stress, void ratio/relative density, number of vibration cycles and cyclic strain history are some of the key parameters that influence the modulus and damping characteristics of sands. Although, the effects of strain amplitude, confining pressure and relative density have been studied quite extensively in literature, only limited studies seem to have been reported in literature to examine the effects of the cyclic strain history and the vibration cycles on these dynamic properties. The objective of this thesis is to study the effects of the cyclic strain history and the number of vibration cycles on the shear modulus and damping ratio of dry sands in a strain range of 0.0001% to 0.1%.
A number of resonant column tests have been performed on dry sand specimens to examine the effect of the cyclic shear strain history, by including both increasing and decreasing strain paths, on the shear modulus and damping ratio for different combinations of relative densities (Dr) and confining pressures (σ3); an increasing strain path intends to simulate a situation when a vibratory machine is just started before reaching a steady state of vibration, and on the other hand, the decreasing strain path matches a condition when the
machine is shut down after running continuously in a steady state for some time. The specimen has been subjected to a series of cycles of increasing and decreasing shear strain paths approximately in a shear strain range of 0.0006% - 0.1%. For chosen values of relative density and confining pressure, two different series of tests beginning with either (i) an increasing strain path or (ii) a decreasing strain path, were performed. In addition, the influence of the numbers of the vibration cycles which are used to measure the resonant frequency of the specimen, referred to as the cycle constant, on the values of shear modulus has also been analyzed.
Irrespective of the strain path adopted to commence the test or the cycle constant used to perform a resonant column test, for a given strain amplitude, the shear modulus along the increasing strain path has been found to be always greater than the corresponding modulus value along the decreasing strain path. For the series of tests which were commenced with the increasing strain path, the shear modulus corresponding to the first increasing strain path becomes always the highest as compared to the subsequent strain paths. For a given strain cycle, irrespective of relative density of sand, the difference between the values of G associated with the increasing and decreasing strain paths becomes always the maximum corresponding to a certain shear strain level. The maximum reduction in the shear modulus, due to the cyclic variation of the shear strain, was noted to be approximately one fourth of the maximum shear modulus (G0). This reduction in the shear modulus, on account of the cyclic variation of the shear strain, increases generally with decrease in the values of both relative density and confining pressure. The damping ratio for a given shear strain for the increasing strain path was noted to be lower than the corresponding value for the decreasing strain path except for the first increasing strain path. For a particular strain level, the series of tests
started with the decreasing strain path resulted in a lower value of shear modulus for all the cyclic strain paths as compared to the tests which were commenced with the increasing strain path. The modulus reduction curve for the first increasing strain path was noted to be more or less the same irrespective of the value of the chosen cycle constant. For the subsequent strain paths, an increment in the cycle constant value caused a reduction in the shear modulus at a particular shear strain level.
In order to match a situation when the machine is running continuously in a steady state of vibration, resonant column tests were conducted in a torsional mode by inducing a large number of the vibration cycles with the shear strain amplitude in a range of 0.0005%-0.05%. Corresponding to a given input voltage of the drive mechanism, the specimens were subjected to a number of vibration cycles ranging from 1,000 to 50,000. The values of shear modulus and damping ratio, before and after the application of vibration cycles, were determined for several input voltages ranging from 0.001 V (minimum) to 0.3 V (maximum). The tests were carried out for different combinations of relative densities and confining pressures. For the chosen relative densities, hardly any influence of vibration cycles on the values of G and D were noted for the strain amplitude below the threshold strain level (0.0024% - 0.0044%). Beyond the threshold strain level, an induction of the vibration cycles leads to a continuous increment in the shear strain which eventually causes (i) a decrease in the shear modulus, and (ii) an increase in the damping ratio. This effect was found to become especially more significant for lower values of relative densities as well as confining pressures. The percentage changes in the values of (i) shear strain, (ii) shear modulus, and (iii) damping ratios after the introduction of vibration cycles were noted to increase with an increment in the number of vibration cycles. However, for a given increment of the vibration
cycles, the changes in the values of shear modulus and damping ratio were generally noted to subside with an increase in the number of the vibration cycles.
At various strain levels, the magnitude of the shear modulus was observed to increase continuously with an increase in the values of both relative density and confining pressure. For the shear strain greater than the threshold strain (0.0024% - 0.0044%), a reduction in the damping ratio values was also noted with an increase in the magnitudes of the confining pressure. On the other hand, the influence of relative density on the damping ratio was found to be relatively negligible. The shear modulus reduction curves from the present tests' data were found to compare reasonably well with the empirical curves proposed in the literature, especially for low values of the confining pressure. A deviation of the present modulus reduction curves from the empirical curves was observed generally at large shearing strains. However, the damping values obtained from the present study were noted to be lower than the values predicted by the existing empirical correlations, particularly for low values of the confining pressure.
An attempt has also been made to improve the accuracy of the measurement of the arrival times of both primary (P) waves and shear (S) waves while conducting bender/extender element tests. For this purpose, a series of laboratory tests were performed on dry sand at different frequencies, varying between 1 kHz and 10 kHz, for medium dense and very dense sands with different values of the confining pressures. While determining the times of arrival of both P and S waves, two corrections have been proposed to incorporate (i) the presence of an initial offset in the input signal, and (ii) the time lag due to an existence of peripheral electronics between the input and received signals when the source and receiver elements are kept in direct contact with each other. The absolute magnitude of the resultant of these two corrections was found to reduce with an increase in the frequency of the input signal. The determination of the P-wave arrival time does not pose much difficulty. It has been noted that it becomes equally accurate to measure the arrival times of the S-wave provided the proposed corrections are incorporated. The maximum shear modulus values measured from the resonant column tests and the bender element tests by incorporating these two corrections were found to compare reasonably well with each other.
The thesis brings out the effects of the cyclic strain history and the vibration cycles on the shear modulus and damping ratio of dry sand. The results obtained are expected to be useful while doing the analysis and design of geotechnical structures subjected to different kinds of vibrations.2017-09-22T18:30:00Z