Pile-up Height Research Articles

Maximum pile-up heights for grounded ice rubble

Large grounded ice features can be found in all regions of the world where there is moving ice. This paper compiles over 230 reported ice pile-ups from several international locations including the Baltic Sea, Gulf of Bothnia, Caspian Sea, Lake Simcoe, Stonehaven Harbour (New Brunswick), west Newfoundland, Alaskan and Canadian Beaufort Sea, Norton Sound, Bering Sea, Somerset Island and offshore Sakhalin. The NRC Particle-in-Cell numerical model is used to augment the data. A plot of the rubble sail height as a function of the ice block thickness shows considerable scatter but a general increase in sail height with increasing ice thickness. The scatter in the data is real and is attributed to the fact that the conditions for producing the maximum sail height are not met in most situations. An upper bound of the data can be represented by Hs,max=19 hB0.33 where Hs,max is the maximum pile-up height (in m), and hB is the block ice thickness (in m). This equation covers the data range up to 2m in ice thickness. The data also clearly show that high pile-ups (on the order of 10 to 12m high) can be generated from thin ice less than 0.5m thick. Further, sail heights up to 30m are possible for thicker sea ice.

Coarse granular flow interaction with slit structures

Coarse grains accumulate in geophysical flow fronts and have high solid fractions. Such fronts may arch in slit structures such as baffles and slit dams, leading to the rapid trapping of particles and potentially high-energy overflow. Existing empirical slit-structure design recommendations are limited and inadequate since they only focus on the slit size to particle diameter ratio (s/δ) and neglect the pileup height and pre-impact flow energy. Flume modelling was thus adopted to study coarse flow fronts impacting a slit structure. The characteristic Froude conditions, flow particle diameter and the ratio s/δ were varied. Results have shown the pileup height, and hence the confining stress is dependent on Froude conditions, but is not strongly influenced by s/δ. The flow particle diameter influences collisional and frictional stresses and hence the mean outflow rate, which is correlated with pileup height. Grain-trapping efficiency depends on both s/δ and Froude conditions. In contrast to existing continuum-based theory for slit-structure interaction, frictional contacts should be considered for coarse-grained flow fronts. High-energy supercritical flows lead to low trapping efficiency since stable arches cannot form at high shear rates. This implies that multiple slit structures may be more appropriate for attenuating high-energy supercritical flows.

Effects of pre-compression deformation on nanoindentation response of Zr65Cu15Al10Ni10 bulk metallic glass

Nanoindentation experiments were conducted on Zr65Cu15Al10Ni10 bulk metallic glass samples with pre-compression deformation (PCD) under various conditions. By analyzing indentation hardness, residual morphology, pile-up, and serrated flow, the effects of PCD on nanoindentation response were comparatively investigated. Experimental results indicate that 9 kN PCD induced remarkable decrease of indentation hardness, i.e. softening of the material, while for the 18 kN and 25 kN PCD samples, hardness values very close to that of the as cast sample were obtained. Furthermore, PCD also changed the mechanical heterogeneity, i.e., distribution of soft and hard regions in the bulk metallic glass. Residual morphologies and load-displacement curves of the 9 kN and 18 kN PCD samples showed opposite features in aspects of macroscopic shear bands, pile-up width, pile-up height, and serrated flows, suggesting different plastic flows during nanoindentation. To rationalize these phenomena, a competing mechanism between shear bands and compressive residual stress was discussed.

Pile-Up Correction of Mechanical Characteristics of Individual Phases in Various Steel by Depth Sensing Indentation

The Oliver–Pharr method has extensively been adopted for measuring hardness and elastic modulus by indentation techniques. However, the method assumes that the contact periphery sinks in, which limits the applicability to the materials pile-up [1]. This study proposes an improved methodology to calculate the real mechanical characteristics of individual phases in various steels with significant pile-up. Pile-up correction of mechanical characteristics is based on ratio of pile-up height and contact depth. Pile-up height was measured by atomic force microscopy (AFM). The effect of grain boundaries on the shape and size of the pile-up lobes was also discussed.

Finite Element Analysis of Deformation Due to Ball Indentation and Evaluation of Tensile Properties of Tempered P92 Steel

Ball indentation (BI) technique has been effectively used to evaluate the tensile properties with minimal volume of material. In the present investigation, BI test carried out on P92 steel (9Cr-0.5Mo-1.8W), using 0.76 mm diameter silicon nitride ball indenter was modeled using finite element (FE) method and analyzed. The effect of test temperature [300 K and 923 K (27 °C and 650 °C)], tempering temperature [1013 K, 1033 K, and 1053 K (740 °C, 760 °C, and 780 °C)], and coefficient of friction of steel (0.0 to 0.5) on the tensile strength and material pile-up was investigated. The stress and strain distributions underneath the indenter and along the top elements of the model have been studied to understand the deformation behavior. The tensile strength was found to decrease with increase in tempering and test temperatures. The increased pile-up around the indentation was attributed to the decrease in strain hardening exponent (n) with increase in the test temperature. The pile-up height determined from profilometry studies and FE analysis as well as the load depth curve from BI and FE analysis was in agreement. The maximum strain location below the indentation changes with the test temperature. Stress–strain curves obtained by conventional tensile, BI test, and representative stress–strain concepts of FE model were found exactly matching.

Erosion investigations by means of a centrifugal accelerator erosion tester

The determination and quantification of hydroabrasion due to the presence of solid particles entrained in the liquid flows is of a great importance in industrial equipment design and maintenance. A centrifugal accelerator erosion tester was designed to investigate the particle dynamics and erosion of different materials under various operating conditions. The tester consisted of a rotating disc to accelerate the slurry flow, gear box and a motor, target holders and a slurry pump to provide a controlled continuous feed of the suspension. The specimen samples were located around the disc on adjustable sample holders. In the present study, a series of experimental tests were carried out to study the effects of disc rotational velocity and feed volumetric flow on the flow impingement angle with the sample plates. The velocity magnitude and angle of slurry flow discharging from the tubes inside the rotating disc could be predicted with respect to the forces affecting the particles. The experimental data were then used to validate the CFD simulation results. The erosion of three various ferrous alloys, an aluminum alloy and a polymer (Hawiflex) were investigated experimentally by variation of influencing parameters. The increase in erosion depth and pileup height by increasing the solid concentration was observed, using a stationary roughness measurement device.

Comparison of Four Different Methods to Determine the Hardness of Plasma-sprayed Cr3C2–NiCr Coating by Nano-indentation

Abstract A Cr3C2–NiCr coating with a thickness of 200 μm was deposited on an AISI 1045 steel substrate using a supersonic plasma-spray technique. The hardness of the Cr3C2–NiCr coating was characterized by a nano-indenter equipped with an atomic force microscope (AFM). The AFM images indicated that the nano-indents on the Cr3C2–NiCr coating exhibited significant “pile-up” deformation. Such pile-up behavior needs to be taken into account in hardness determination because the pile-up height accounts for a large proportion of the indentation depth. In this paper, four different methods are compared to determine the hardness of the Cr3C2–NiCr coating: the Oliver–Pharr method, two work-of-indentation methods (total work of indentation and plastic work of indentation), and an AFM analysis method. The results show that the Oliver–Pharr and work-of-indentation methods overestimated the hardness, and the AFM analysis method is considered as a more accurate method for determining the hardness of the Cr3C2–NiCr coating.

The effect of work-hardening and pile-up on nanoindentation measurements

Nanoindentation is performed on the cross-section of copper samples subjected to surface mechanical attrition treatment (SMAT). The cross-section of the SMAT samples provides a unique microstructure with varying amounts of work-hardening depending on the distance from the SMAT surface. Results show that for a given indentation load the pile-up height decreases and the indentation depth increases as the distance from the SMAT surface increases, both following a power law relationship. Based on image analysis of the indented surface this increase in the pile-up height and decrease in indentation depth is attributed to the localization of plastic strain due to the increased resistance to dislocation motion in the work-hardened region. For a given amount of work-hardening (in terms of distance from SMAT surface), the indentation depth increased with the indentation load obeying a power law relationship with the exponent ranging from 0.58 to 0.68. However, the pile-up height increased linearly with the load, with the rate (slope) increasing with the amount of work-hardening. The observed linear increase in pile-up height with indentation load would naturally introduce an indentation size effect (ISE) if the hardness is corrected for the pile-up. Interestingly, this ISE associated with pile-up increased with an increase in indentation depth, in contradiction to the ISE associated with strain gradient. Deviation of the hardness values corrected for pile-up from the bulk behavior due to surface effect is highlighted and a method to obtain a bulk-equivalent hardness quantity representing the bulk behavior is proposed.

Effect of Pile-Up on the Mechanical Characteristics of Steel by Depth Sensing Indentation

Mechanical properties by depth sensing indentation are derived from the indentation load-displacement data used a micromechanical model developed by Oliver & Pharr (O&P). However, O&P analysis on the indentation unloading curve is developed from a purely elastic contact mechanics (sink-in). The applicability of O&P analysis is limited by the materials pile-up. However, when it does, the contact area is larger than that predicted by elastic contact theory (material sinks-in during purely elastic contact), and both hardness H and Youngs modulus E are overestimated, because their evaluation depends on the contact area deduced from the load-displacement data. H can be overestimated by up to 60 % and E by up to 30 % depending on the extent of pile-up [1,2]. It is therefore important to determine the effect of pile-up on obtained mechanical characteristics of the material by depth sensing indentation. The work experimentally analyses the effect of pile-up height on mechanical characteristics H and E, which are determined by O&P analysis. Pile-up height was measured by atomic force microscopy (AFM).

Generalised Wagner model of water impact by numerical conformal mapping

A numerical method to solve the problem of symmetric rigid contour entering water vertically at a given time-dependent speed is presented. The method is based upon the so-called generalised Wagner model. Within this model the body boundary condition is imposed on the actual position of the entering surface, the free-surface boundary conditions are linearised and imposed on the pile-up height, which is determined as part of the solution. The hydrodynamic pressure is given by the non-linear Bernoulli equation. The hydrodynamic pressures which are below the atmospheric value are disregarded. The conformal mapping of the flow region onto the lower half-plane is used. The velocity potential of the flow is given in analytical form once this mapping is known. The conformal mapping is calculated numerically. The obtained results are validated with respect to the known solutions for wedge and circular cylinder. The novelty and practical importance of the present approach are due to a special accurate treatment of the flows and the pressures close to the contact points between the entering body and water free surface. This special treatment is required for reliable prediction of the hydrodynamic pressure along the wetted part of the contour during its impact onto the water surface and the subsequent entry.

Pileup Behavior in Sharp Nanoindentation of AISI 1045 Steel

Abstract Experimental measurements have been used to investigate the pileup behavior during nanoindentation with a sharp indenter. The AISI 1045 steels treated by quenching and annealing were examined. The results show that during sharp nanoindentation process, the amount of pileup is related to the residual stress state, the indentation depth and the work hardening. The quenched steel with compressive residual stress will tend to pile up, and the stress-free annealed steel can decrease the pileup height. It is found that the pileup height gradually increases for the two steels as the indentation depth becomes larger. It is also shown that the low work hardening of the two steels can also result in the pileup deformation.

Analytical Model for Plowing Friction at Nanoscale

Existing analytical models for elastic–plastic friction, which have been developed for microscale single-asperity contacts, do not apply when the contact dimensions are reduced to the nanometer regime. We demonstrate that although the microscale models correctly describe elastic recovery behind a sliding nanoscale tip, they fail to predict the corresponding coefficient of friction. We show that the breakdown of microscale models can be attributed to the large contribution to friction from pileup. We propose an analytical model for plowing friction for single-asperity contacts, which includes the effects of both elastic recovery and pileup. Functional dependence of the average pileup height on elastic properties of the worn material and on the depth of cut is also proposed. Applicability of the new model is demonstrated in the examples of SiC and Cu.

Deformation, structural changes and damage evolution in nanotwinned copper under repeated frictional contact sliding

Nanotwinned metals have the potential for use as structural materials by virtue of having a combination of high strength as well as reasonable ductility and damage tolerance. In the current study, the tribological response of nanotwinned copper has been characterized under conditions of repeated frictional sliding contact with a conical tip diamond indenter. Pure ultrafine-grained copper specimens of fixed grain size (∼450nm), but with three different structural conditions involving relatively high, medium and negligible concentrations of nanotwins, were studied. The effects of twin density and number of repetitions of sliding cycles on the evolution of friction and material pile-up around the diamond indenter were studied quantitatively by depth-sensing instrumented frictional sliding. Cross-sectional focused ion beam and scanning electron microscopy observations were used to systematically monitor deformation-induced structural changes as a function of the number of passes of repeated frictional sliding. Nanoindentation tests at the base of the sliding tracks coupled with large-deformation finite-element modeling simulations were used to assess local gradients in mechanical properties and deformation around the indenter track. The results indicate that friction evolution as well as local mechanical response is more strongly influenced by local structure evolution during repeated sliding than by the initial structure. An increase in twin density is found to result in smaller pile-up height and friction coefficient. Compared to the low-density nanotwinned metal, high-density nanotwinned copper showed significantly higher resistance to surface damage and structural changes, after the initial scratch. However with an increase in the number of sliding passes, the friction coefficient and rate of increase of pile up for all specimens acquire a steady value which does not change significantly in subsequent scratch passes. The frictional sliding experiments also lead to the striking result that copper specimens with both a high and low density of nanotwins eventually converge to a similar microstructure underneath the indenter after repeated tribological deformation. This trend strongly mirrors the well-known steady-state response of microcrystalline copper subjected to uniaxial cyclic loading. General perspectives on contact fatigue response of nanotwinned copper are developed on the basis of these new findings.

Identification of the material properties of Al 2024 alloy by means of inverse analysis and indentation tests

► Identification of mechanical properties by indentation test and inverse analysis. ► Pile-up height is also considered as experimental information. ► Inverse problem results to be well posed also in the case of mystical materials. ► 2024 Al alloy samples prepared using different age-hardening treatments are studied. This paper outlines an inverse analysis approach aimed at the identification of the mechanical properties of metallic materials based on the experimental results obtained from indentation tests. Previous work has shown the ill-posed nature of the inverse problem based on the load-penetration curve when dealing with mystical materials, which exhibit identical indentation curves even if possessing different yield and strain-hardening properties. For this reason, an additional measurement is used in the present study as input for the inverse analysis which consists of the maximum pile-up height measured after the indentation test. This approach lends itself for practical applications as the load-penetration curve can be easily obtained from commonly available micro-indenters while the pile-up present at the end of the test can be measured by different instruments depending on the size of the indented area, for example by means of an atomic force microscope or a laser profilometer. The inverse analysis procedure consists of a batch deterministic approach, and conventional optimization algorithms are employed for the minimization of the discrepancy norm. The first part of the paper outlines how the inclusion of both the maximum height of the pile-up and the indentation curve in the input data of the inverse analysis leads to a well-defined inverse problem using parameters of mystical materials. The approach is then applied to real experimental data obtained from three sets of 2024 Al alloy samples prepared using different age-hardening treatments. The accuracy of the identification process is validated against the mechanical properties obtained independently from standard tensile coupon tests. The reported results highlight the advantages of the proposed methodology in identifying the elastic modulus, yield stress and strain-hardening coefficient while minimizing the amount of information required to be collected from the experimental indentation tests.

Experimental and numerical investigations of single abrasive-grain cutting

The present work will provide an in-depth analysis of the abrasive-grain cutting process using a combination of experimental observations and finite element simulations. The workpiece material was AISI 4340. The cutting tool was spherical in shape with a 0.508 mm radius and was fabricated from diamond. The experiments were conducted at cutting speeds of 5−30 m/s in 5 m/s increments and depths of cut from 0.3 to 7.5 μm. The analysis provided a comprehensive understanding of the abrasive-grain cutting process related to the friction between the cutting tool and the workpiece, the material mechanics of the workpiece, and the cutting mechanics of the operation. It was found that the normal forces increased as cutting speed increased due to strain-rate hardening of the workpiece and that the tangential forces decreased as cutting speed was increased due to a reduction in tool-workpiece friction and due to a change in cutting mechanics. The scratch profiles showed that the cutting mechanics changed as cutting speed was increased due to a reduction in material pile-up height. The approximate uncut chip thicknesses for the transitions from elastic, elastoplastic, and fully plastic cutting were identified and were found to increase as cutting speed was increased.

Ultra-mild wear mechanisms of Al–12.6wt.% Si alloys at elevated temperature

Abstract An internal combustion engine made of Al–Si alloys should operate in ultra-mild wear (UMW) regime. The objective of this work was to understand the wear mechanisms operating in Al–12.6 wt.% Si alloys tested at 100 °C under boundary lubricated condition simulating UMW regime. The sliding tests were conducted on surfaces etched to protrude silicon above the aluminum surface and optical profilometery was used to analyze changes in Si morphology during sliding. Three different stages of UMW were identified. During UMW-I, formation of a discontinuous island-like tribofilm primarily consisting of zinc sulphide from lubricating oil on top of silicon particles was observed and silicon particles progressively became embedded in the matrix. A criterion for transition between UMW-I and UMW-II was developed in terms of the ratio of pile-up height to silicon height. In UMW-II, the piled-up aluminum started to wear and an approximately 100–150 nm thick continuous oil-residue layer (ORL) formed on the worn surface primarily consisting of smeared island-like tribofilm mixed with aluminum. The ORL was also supported by a sliding induced ultrafine grain aluminum layer, and consequently microstructure evolution led to a stabilized surface with lower wear loss in UMW-III compared to UMW-II. UMW-III wear rates at 100 °C were similar to those at 25 °C.

Measurement of mechanical properties of 1045 steel with significant pile-up by sharp indentation

The Oliver–Pharr method has extensively been adopted for measuring hardness and elastic modulus by indentation techniques. However, the method assumes that the contact periphery sinks in, which limits the applicability to the materials pile up. This study proposed an improved methodology to calculate the real contact area of 1045 steel with significant pile-up. The contact boundary between indenter and specimen was assumed to overlap with the top points on the residual surface profile, and the real contact depth was defined by a sum of the indentation depth at maximum load, hmax, and average pile-up height, \( h_{\text{pile - up}}^{\text{ave}} \), measured from the analysis on the residual indent morphology with atomic force microscope (AFM). The mechanical properties calculated by the newly proposed method were compared with those by the Oliver–Pharr method.

A new method for evaluating the plastic properties of materials through instrumented frictional sliding tests

Frictional normal contact probing methods involving instrumented, depth-sensing indentation can be used to estimate the mechanical properties of small-volume structures and materials such as thin films and components of micro-electro-mechanical systems. This paper describes a new method for estimating the plastic properties, i.e. the yield strength and strain hardening exponent, of ductile materials from the topography of scratches formed by a conical tip during an instrumented, depth-sensing frictional sliding test. The proposed reverse analysis (or inverse analysis) uses dimensionless functions derived from computational simulations to extract plastic properties from an instrumented scratch response performed on a standard, commercially available instrument. Sensitivity analysis indicates that an experimental error of 5% in the scratch hardness or the pile-up height induces an error of <22% in the estimated strain hardening exponent. Laboratory experiments illustrate how two aluminum alloy tempers of the same indentation hardness have significantly different pile-up as a result of different strain hardening. Comparative results between the frictional sliding test and traditional tensile tests showed reasonable agreement for a total of 11 metallic alloys evaluated. These results confirm the potential usefulness of the proposed method as an engineering tool to probe plastic properties of small-volume materials and confined structures where it is difficult to obtain reliable estimates of mechanical properties by other means.

A simple method to evaluate anisotropic plastic properties based on dimensionless function of single spherical indentation – Application to SiC whisker-reinforced aluminum alloy

In this study, an evaluation method for anisotropic plastic properties is proposed using dimensional analysis of single spherical indentation. The method considers a plastically anisotropic material, whose properties are different among orthogonal directions (e.g. longitudinal and transverse direction). In other words, the stress–strain curves along both directions can be simultaneously determined by the present method. When a spherical indenter is impressed against a plane cut along the longitudinal direction (i.e. indentation was conducted along the transverse direction), the impression geometry was found to change depending on the orthogonal axis. That is, the pile-up height in the transverse direction becomes higher than that in the longitudinal one. Using this characteristic and the indentation curve, dimensional functions were established in order to deduce anisotropic plastic properties. Extensive finite element analysis was first carried out to compute the indentation response (indentation curve and impression geometry). Subsequently, dimensionless functions connecting the anisotropic plastic properties to the indentation response were established. The effectiveness of the method was verified by numerical experiments. Finally, an indentation experiment was carried out on an SiC whisker-reinforced aluminum alloy to deduce the anisotropic plastic properties. The estimation results were found to be reliable. The present method is thus useful for determining the plastic properties of various anisotropic materials, such as cold-worked steel, composites and coatings.

Estimation of the anisotropic plastic property using single spherical indentation—An FEM study

Abstract In this study, a method to evaluate the in-plane anisotropic plastic properties of engineering steels by single spherical indentation is proposed. This method deals with materials that obey the work hardening law and have in-plane anisotropy of the yield stress in orthogonal directions. The method thus estimates the yield stress σ Y , the work hardening exponent n , and the ratio of the yield stresses m . Computations were first carried out by the finite element method (FEM) in order to quantitatively study the deformation surrounding the impression, when the spherical indenter was pressed against the anisotropic plastic materials. The permanent impression that remained after fully unloading the indenter was found to be non-uniform. The pile-up height in the direction of lower yield stress becomes higher than that in the direction of high yield stress. Such differences in height were found to become larger when m is higher. Based on this characteristic, extensive FEM calculations were carried out in order to propose the method to identify the anisotropic plastic properties for various materials whose mechanical properties are available for many engineering steels. The method involves several functions that relate the indentation response (indentation curve and geometry of impression) to the anisotropic plastic property of the material. Numerical experiments were conducted in order to verify the effectiveness of the proposed method.