Pile-up Patterns Research Articles

Deformation Mechanisms of (100) and (110) Single-Crystal BCC Gum Metal Studied by Nanoindentation and Micropillar Compression

AbstractIn this paper, small-scale testing techniques—nanoindentation and micropillar compression—were used to investigate the deformation mechanisms, size effects, and strain rate sensitivity of (100) and (110) single-crystal Gum Metal at the micro/nanoscale. It was observed that the (100) orientation exhibits a significant size effect, resulting in hardness values ranging from 1 to 5 GPa. Conversely, for the (110) orientation, this effect was weaker. Furthermore, the yield strength obtained from the micropillar compression tests was approximately 740 MPa for the (100) orientation and 650 MPa for the (110) orientation. The observed deformations were consistent with the established features of the deformation behavior of body-centered cubic (bcc) alloys: significant strain rate sensitivity with no depth dependence, pile-up patterns comparable to those reported in the literature, and shear along the {112}<111> slip directions. However, the investigated material also exhibited Gum Metal-like high ductility, a relatively low modulus of elasticity, and high yield strength, which distinguishes it from classic bcc alloys.

Slip responses and pre-twin structure evolution based on indentation pile-up in magnesium single crystal

Slip behavior and microstructure evolution caused by the indentation pile-up deformation were studied in Mg single crystal with {10–12} pre-twin structure at room temperature. The anomalous indentation is formed on the surface of the large-size single crystal. It is attributed to plastic flow induced by the combined effects of dislocation slip, detwinning and {10–12} twinning during indentation. At the early stage of indentation, basal slip dominates the pile-up deformation. And the reaction structure of basal slips, i.e. (0001) slip plane in the twin to correspond to (0001) slip plane in the matrix, is frequently formed on the twin boundary in order to facilitate plastic relaxation of the local stress on the twin boundary. Under pile-up pattern, the stress state favors detwinning. And detwinning behavior is subjected to effects of stress-field magnitude and pre-twin size. For the little-volume and large-volume pre-twins, detwinning behaviors play the modes of twin shrinkage and “local detwinning” respectively. The latter might involve reverse nucleation and growth of matrix. Although pile-up pattern is unfavorable to {10–12} twinning, stress concentration caused by the interaction between slip dislocations and twin boundary induces the local twin growth on the interface. In addition, a pyramidal slip is found in matrix, and its slip trace is corresponding to (0001) slip trace in twin.

The Influence of Crystallographic Orientation and Grain Boundary on Nanoindentation Behavior of Inconel 718 Superalloy Based on Crystal Plasticity Theory

The crystal plasticity finite element method (CPFEM) is widely used to explore the microscopic mechanical behavior of materials and understand the deformation mechanism at the grain-level. However, few CPFEM simulation studies have been carried out to analyze the nanoindentation deformation mechanism of polycrystalline materials at the microscale level. In this study, a three-dimensional CPFEM-based nanoindentation simulation is performed on an Inconel 718 polycrystalline material to examine the influence of different crystallographic parameters on nanoindentation behavior. A representative volume element model is developed to calibrate the crystal plastic constitutive parameters by comparing the stress-strain data with the experimental results. The indentation force-displacement curves, stress distributions, and pile-up patterns are obtained by CPFEM simulation. The results show that the crystallographic orientation and grain boundary have little influence on the force-displacement curves of the nanoindentation, but significantly influence the local stress distributions and shape of the pile-up patterns. As the difference in crystallographic orientation between grains increases, changes in the pile-up patterns and stress distributions caused by this effect become more significant. In addition, the simulation results reveal that the existence of grain boundaries affects the continuity of the stress distribution. The obstruction on the continuity of stress distribution increases as the grain boundary angle increases. This research demonstrates that the proposed CPFEM model can well describe the microscopic compressive deformation behaviors of Inconel 718 under nanoindentation.

Nanoindentation size effects of mechanical and creep performance in Ni-based superalloy

Nanoindentation technique was adopted to study indentation size effects of physical-mechanical and creep performance with various depths (200–2000 nm) in GH901 utilising sharp and spherical tip. Residual impressions of both indenters with pile-up patterns are discussed. Nanohardness, reduced modulus and elastic recovery rates curves versus maximum displacement of two tips are obtained and nanohardness size effects are discussed with different models for Berkovich tip. The data obtained with spherical indentation are analysed separately by establishing stress–strain diagram. The creep results using Berkovich tip indicate that creep strain rate declines while creep stress exponent first decreases and then increases with the increasing depth; the creep stress exponent (n) values, 2.39–7.35, imply the dominant creep deformation mechanism is dislocation control.

Inverse Identification of Single-Crystal Plasticity Parameters of HCP Zinc from Nanoindentation Curves and Residual Topographies.

This paper investigates the orientation-dependent characteristics of pure zinc under localized loading using nanoindentation experiments and crystal plasticity finite element (CPFEM) simulations. Nanoindentation experiments on different grain orientations exhibited distinct load–depth responses. Atomic force microscopy revealed two-fold unsymmetrical material pile-up patterns. Obtaining crystal plasticity model parameters usually requires time-consuming micromechanical tests. Inverse analysis using experimental and simulated loading–unloading nanoindentation curves of individual grains is commonly used, however the solution to the inverse identification problem is not necessarily unique. In this study, an approach is presented allowing the identification of CPFEM constitutive parameters from nanoindentation curves and residual topographies. The proposed approach combines the response surface methodology together with a genetic algorithm to determine an optimal set of parameters. The CPFEM simulations corroborate with measured nanoindentation curves and residual profiles and reveal the evolution of deformation activity underneath the indenter.

On the Pile-Up and Sink-in Behavior of Indented Nickel Considering Dislocation Structures

Background: Surface topography of pile-up and sink-in is an issue of strain-hardening behavior around pyramidal and spherical indentations. The relationship between the surface profile and the activated dislocations is not clearly understood. Objective: This study combined electron channeling contrast imaging (ECCI), electron backscatter diffraction-based (EBSD) techniques and 3D laser microscopy to visualize the stress field and understand the influence of activated dislocations on the surface topography around an indent. Methods: The dislocation structures were identified using ECCI and geometrically necessary dislocation (GND) analysis. The stresses and GND densities were calculated to characterize the plastic deformation in terms of activated dislocations. The 3D laser microscopy was applied to reveal the surface topography. Results: The activated slip systems were identified as screw-type on $$ \left(1\overline{1}\overline{1}\right)\left[110\right] $$ , $$ \left(1\overline{1}\overline{1}\right)\left[101\right] $$ , $$ \left(\overline{1}1\overline{1}\right)\left[011\right] $$ , $$ (111)\left[\overline{1}10\right] $$ and $$ (111)\left[10\overline{1}\right] $$ slip systems, and edge-type on $$ \left(1\overline{1}\overline{1}\right)\left[101\right] $$ , $$ \left(\overline{1}1\overline{1}\right)\left[\overline{1}01\right] $$ and $$ \left(\overline{1}\overline{1}1\right)\left[\overline{1}0\overline{1}\right] $$ slip systems by combining ECCI and GND techniques. Furthermore, the surface morphology reveals a combination of pile-up and sink-in patterns around the indent, as observed by 3D laser microscopy. According to GND analysis, pile-up is generated from the $$ \left(1\overline{1}\overline{1}\right)\left[\overline{1}\overline{1}0\right] $$ , $$ (111)\left[1\overline{1}0\right] $$ , $$ \left(1\overline{1}\overline{1}\right)\left[101\right] $$ and $$ \left(\overline{1}\overline{1}1\right)\left[101\right] $$ slip systems, and sink-in is caused by the $$ \left(\overline{1}1\overline{1}\right)\left[0\overline{1}\overline{1}\right] $$ , $$ \left(1\overline{1}\overline{1}\right)\left[\overline{1}0\overline{1}\right] $$ , and $$ \left(\overline{1}1\overline{1}\right)\left[10\overline{1}\right] $$ . Conclusions: The surface profile reveals a combination of pile-up and sink-in patterns resulting in the activated dislocations, where the deformation around the indent is dominated by screw-type dislocations.

Size Effect in Single Crystal Copper Examined with Spherical Indenters

The increasing hardness with decreasing penetration depth, referred to as indentation size effect (ISE) was previously investigated experimentally and theoretically by many researchers, however the mechanisms responsible for ISE are still being discussed. Generally, ISE is related to the density of geometrically necessary dislocation stored within a small volume beneath the indenter tip. In this study ISE is investigated experimentally in a single crystal copper using spherical indenter tips of different radii. Some new aspects of ISE are shown: a qualitative change of shape of residual impression (pile-up/sink-in pattern) when tip radius or load is modified, an increase of maximum pop-in load with decrease of tip radius as well as the well-known increase of hardness when tip radius decreases are analyzed. As we observe a difference of the residual imprint morphology which depends on tip radius and load, we apply two methods of hardness estimation: true hardness and nominal hardness. The former is determined on the basis of direct measurement of the contact area while accounting for a specific pile-up pattern, while the latter is determined by measuring the contact area using residual penetration depth. We show that hardness–tip radius relationship has a linear form for the nominal hardness and bilinear form for the true hardness.

Experimental observations on the ice pile-up in the conductor array of a jacket platform in Bohai Sea

Massive ice pile-ups have been frequently observed in the conductor array of offshore jacket platforms in Bohai Sea. Once formed, such rubble piles were very difficult to clear manually and therefore studies on the ice rubble piles and their forming process were needed. This study investigates the ice pile-up behavior in the conductor array of a jacket platform in Bohai Sea by conducting a series of model tests in the ice tank at Tianjin University. The laboratory-scale model jacket was mounted on a rigid carriage and towed through the ice sheet at different speeds, directions and water levels. Observations on the test phenomena indicated that the water level and ice attack direction had a significant influence on the ice failures in front of the ice-breaking cones and the conductor array, thereby resulting in different ice pile-up patterns in the conductor array. The ice drift velocity only affects the pile-up dimensions, normally higher ice velocity resulting in higher pile-up heights. Also, based on the measured ice pile-up dimensions, the distribution of the ice rubble pile in the conductor array was found to be non-homogeneous, both laterally and longitudinally, and the rubble pile was found “grounded” on the bottom of the model conductor array in some cases, which might bring about additional load to the jacket structure. Furthermore, the horizontal ice forces acting on the conductor array due to ice rubble building were also measured, and comparisons of the ice forces based on the present tests with the calculated results from ISO algorithm were made. The R value of 5–6 might be more applicable for the present structure under the present ice conditions.

Berkovich nanoindentation study of monocrystalline tungsten: a crystal plasticity study of surface pile-up deformation

In this paper, it was investigated whether Berkovich indentation test with a triangular-based pyramidal imprint would exhibit the same surface pile-up deformation behaviour as in Vickers or spherical indentation tests. The characteristic correlation between the pile-up patterns of monocrystalline tungsten and the geometry of slip systems was examined both experimentally and computationally. Surface pile-up patterns for three different crystallographic orientations of specimens with corresponding rotational crystal symmetry were characterised. In addition, the effect of the varying azimuthal orientation of the indenter on the pile-up patterns was also discussed. Predictions from finite element simulation based on the crystal plasticity theory are also presented and compared with the measured results. It was found that the surface pile-up patterns of Berkovich indentation did not necessarily reflect the rotational crystal symmetry of tungsten single crystal specimens. The pile-up patterns were affected by the variation of the indenter’s azimuthal orientation. The height of the pile-up hillocks was often highly non-uniform even on the same surface plane indicating strong influence of slip geometry leading to the plastic anisotropy.

Indentation Pileup Behavior of Ti-6Al-4V Alloy: Experiments and Nonlocal Crystal Plasticity Finite Element Simulations

This study reports on the indentation pileup behavior of Ti-6Al-4V alloy. Berkovich nanoindentation was performed on a specimen with equiaxed microstructure. The indented area was characterized by electron backscattered diffraction (EBSD) to obtain the indented grain orientations. Surface topographies of several indents were measured by atomic force microscopy (AFM). The pileup patterns on the indented surfaces show significant orientation dependence. Corresponding nonlocal crystal plasticity finite element (CPFE) simulations were carried out to predict the pileup patterns. Analysis of the cumulative shear strain distributions and evolutions for different slip systems around the indents found that the pileups are mainly caused by prismatic slip. The pileup patterns evolve with the loading and unloading process, and the change in pileup height due to the elastic recovery at unloading stage is significant. The density distributions of geometrically necessary dislocations (GNDs) around the indent were predicted. Simulation of nanoindentation on a tricrystal model was performed.

Unraveling deformation mechanisms around FCC and BCC nanocontacts through slip trace and pileup topography analyses

Nanocontact loadings offer the potential to investigate crystal plasticity from surface slip trace emissions and distinct pileup patterns where individual atomic terraces arrange into hillocks and symmetric rosettes. Our MD simulations in FCC Cu and Al nanocontacts show development of specific dislocation interception, cross-slip and twin annihilation mechanisms producing traces along characteristic <011> and <112> directions. Although planar slip is stabilized through subsurface dislocation interactions, highly serrated slip traces always predominate in Al due to the advent of cross-slip of the surfaced population of screw dislocations, leading to intricate hillock morphologies. We show that the distinct wavy hillocks and terraces in BCC Ta and Fe nanocontacts are due to dislocation double-kinking and outward spreading of surfaced screw segments, which originate from dislocation loops induced by twin annihilation and twin-mediated nucleation processes in the subsurface. Increasing temperature favors terrace formation in BCCs whereas the enhancement of surface decorations in FCCs limits hillock definition. It is found that material bulging against the indenter-tip is a distinctive feature in nanocontact plasticity associated with intermittent defect bursts. Bulging is enhanced by recurrent slip traces introduced throughout the contact surface, as in the case of the strongly linear defect networks in FCC Al, and by specific twin arrangements at the vicinity of BCC nanocontacts. Defect patterning also produces surface depressions in the form of vertexes around FCC nanoimprints. While the rosette morphologies are consistent with those assessed experimentally in greater FCC and BCC imprints, local bulging promoted during tip removal becomes more prominent at the nanoscale.

Finite element implementation of dislocation-density-based crystal plasticity model and its application to pure aluminum crystalline materials

A new time-integration algorithm is presented for a dislocation-density-based crystal plasticity model. This includes a monolithic iterative scheme in which stresses were solved simultaneously with dislocation densities based on the fully backward Euler method for the integration of the constitutive model. Furthermore, the heuristic convergence criterion based on the slip resistance, instead of dislocation densities, together with the stresses is employed to circumvent stability issues. A closed form of the consistent tangent moduli is also derived. The constitutive models and time-integration procedures have been implemented as a user-subroutine UMAT of a finite element program Abaqus. Representative comparisons between the numerical predictions and experimental data are then given to verify the robustness and stability of the current implementation of the dislocation-density-based crystal plasticity model. It is demonstrated that finite element calculations reproduce well the anisotropic hardening response of differently oriented pure aluminum single crystals under tension and the variation of pile-up patterns according to different initial crystallographic orientations during nanoindentation. Furthermore, the numerical procedure was used to predict the deformation response of the aluminum multicrystalline specimen under simple shear. Non-uniform deformation fields by the digital image correlation method and surface profiles by the shadow Moiré method were well reproduced by numerical predictions. In addition, the effect of the initial crystallographic orientation and the interaction effects among different crystals on the deformation response of the multicrystal are addressed.

Micro-cutting of single-crystal metal: Finite-element analysis of deformation and material removal

This paper presents analysis of mechanics in a micro-cutting process of a single-crystal metal – mechanisms of deformation and material removal related to an anisotropic crystallographic structure of a work-piece. A crystal-plasticity theory was implemented in a finite-element (FE) modelling scheme to consider inherently anisotropic deformation of a single-crystal metal at micro-scale. A new shear-strain-based criterion and several conventional strain-based criteria were employed to simulate the material removal process, and their effect on the anisotropy of cutting forces was studied. Subsequently, the micro-cutting process of single-crystal copper was predicted using FE modelling by combining the crystal-plasticity theory and the proposed criterion of material removal. The validity of the present FE modelling methodology was corroborated through a comprehensive comparison between FE simulations and experimental data in terms of cutting forces, chip morphology, deformation field, pile-up patterns and misorientation angle in the work-piece.

Multi-scale simulation of nanoindentation on cast Inconel 718 and NbC precipitate for mechanical properties prediction

Multi-scale simulation of nanoindentation on cast Inconel 718 superalloy and its NbC precipitate were performed with combined first principle study and crystal plasticity finite element method (CPFEM). The concerned parameters were calibrated through a representative volume element (RVE) model compared with the stress–strain curves obtained from tensile tests. Nanoindentation was carried out on the matrix. First principle calculations were applied to estimate the mechanical properties of precipitate NbC, including elastic modulus and hardness. The simulated force–displacement curves match well with the experimental results. The simulated results indicate that the local pile-up pattern in the indentation zone depends significantly on the crystallographic orientations. In addition, large precipitate NbC inserted in the matrix was also indented and simulated. The elastic modulus calculated by first principle is quite accurate while the yield stress is determined using inversion calculations. It appears that the proposed CPFE analysis approach combined with first principle calculation do help estimate the mechanical behavior of large precipitates on the Ni-based superalloy.

Decrease of Nano-hardness at Ultra-low Indentation Depths in Copper Single Crystal

In the present study, we report a detailed investigation of the unusual size effect in single crystals. For the experiments we specified the hardness in single crystalline copper specimens with different orientations ((001), (011) and (111)) using Oliver-Pharr method. Our results indicates that with decreasing load, after the value of the hardness reached its maximum, it starts to decrease for very small indentation depths (<150 nm). For the sake of accuracy of hardness determination we have developed two AFM-based methods to evaluate contact area between tip and indented material. The proposed exact measurement of the contact area, which includes the effect of pile-up and sink-in patterns, can partially explain the strange behaviour, however, the decrease of hardness at low loads is still observed. At higher loads range the specified hardness is practically constant.

A combined experimental-numerical approach for determining mechanical properties of aluminum subjects to nanoindentation.

A crystal plasticity finite element method (CPFEM) model has been developed to investigate the mechanical properties and micro-texture evolution of single-crystal aluminum induced by a sharp Berkovich indenter. The load-displacement curves, pile-up patterns and lattice rotation angles from simulation are consistent with the experimental results. The pile-up phenomenon and lattice rotation have been discussed based on the theory of crystal plasticity. In addition, a polycrystal tensile CPFEM model has been established to explore the relationship between indentation hardness and yield stress. The elastic constraint factor C is slightly larger than conventional value 3 due to the strain hardening.

Explore the anisotropic indentation pile-up patterns of single-crystal coppers by crystal plasticity finite element modelling

We report a new in-depth explanation of the anisotropic pile-up phenomenon based on the plastic slip theory. A crystal plasticity finite element method (CPFEM) model which considers plastic slips and lattice rotations as the only deformation mechanism has been developed to investigate the anisotropic pile-up behaviour of (001), (011) and (111) initially orientated single-crystal copper (Cu) undergoing nanoindentation. It is concluded that the activation of different slip systems contributes to the anisotropy of pile-up patterns.

Crystal plasticity FEM study of nanoindentation behaviors of Cu bicrystals and Cu–Al bicrystals

Abstract

Experiments and crystal plasticity finite element simulations of nanoindentation on Ti–6Al–4V alloy

Abstract In this paper, we investigated the micromechanical behavior of Ti–6Al–4V by means of nanoindentation experiments performed on a specimen with duplex microstructure. After nanoindentation experiments, electron backscattered diffraction (EBSD) scan was conducted on the nanoindentation region to obtain the crystallographic information. Then the crystal plasticity finite element (CPFE) simulations were carried out using the measured grain orientations. The simulated load–displacement curves match the experimental data well with proper model parameters. It was found that the hardness varied with the grain orientation, and the pileup patterns on the indented surfaces exhibit significant anisotropy and grain orientation dependence. The effects of grain boundary and orientation of Berkovich indenter on the nanoindentation results were discussed.

Depth Dependence of Nanoindentation Pile-Up Patterns in Copper Single Crystals

Abstract A study of the dependence of nanoindentation pile-up patterns on the indentation load and crystallographic orientation is presented. Three different orientations—(001), (011), and (111)—of single crystal copper were investigated. Experiments were conducted on a CSM ultra-nanoindentation tester using a Berkovich tip. The topographic images were obtained using an atomic force microscope. The evolution of pile-up patterns with different applied loads was observed. The results show that for applied loads equal to 0.45 mN and smaller the pile-up patterns do not depend on the crystallographic orientation of the indented surface; instead, they depend on the tip’s geometry. On the other hand, in the case of indentation loads bigger than 2 mN, pile-up patterns on the surfaces of (001)-, (011)-, and (111)-oriented single crystals have fourfold, twofold, and sixfold (or threefold) symmetry, respectively. An intermediate state was also reported. Furthermore, a detailed analysis of residual impressions with maximal applied loads equal to 2 mN and bigger reveals that both pile-up and sink-in patterns are present.