Indentation Force Research Articles

Numerical investigation on rock fragmentation during indentation with a conical pick based on discrete element method

This article investigates the fragmentation of rock during the indentation process with a conical pick. The study explores the impact of indentation dip angle, indentation spacing, and confining pressure on rock fragmentation through simulation using the discrete element method. Rock models of coal and red sandstone are created and calibrated for the simulation. The findings indicate that the indentation force increases exponentially with the increase of indentation dip angle for both coal and red sandstone. The specific energy increases first and then decreases with the increase of indentation dip angle. The maximum specific energy is found in the condition of indentation dip angle of 25° for red sandstone, while it is 20° for coal. The indentation force increases logarithmically with the increase of indentation spacing tending to be an unrelieved indentation condition. The optimal indentation spacing with the lowest specific energy is determined to be 50 mm for breaking coal and 34 mm for breaking red sandstone. Additionally, the indentation force increases exponentially for coal while it increases linearly for red sandstone with the increase of the confining pressure. For both coal and red sandstone, specific energy increases with the increase of the confining pressure.

Simulation and experimental study on surface modification of 6061‐T651 aluminum alloy by machine hammer peening

AbstractMachine hammer peening is a surface treatment technique employed to enhance the surface properties of the treated samples. In this present work, the theoretical analysis, finite element simulation and experiment of single peening are carried out to investigate the relationship between the machine hammer peening force and geometric dimensions of the single peening indentation deformation, including diameter and depth. The single peening experimental results are in accordance with theoretical and simulation analysis. The machine hammer peening experiment with grate tool path are done and the results including surface topography, surface roughness, surface hardness, x‐ray diffraction analysis and wear resistance are discussed. This work seeks to explore the effects of process parameters like machine hammer peening force, indentation and pitch spacing on surface roughness and hardness. The results reveal that the surface hardness and roughness are positively associated with machine hammer peening force and small indentation and pitch spacing lead to high hardness. The x‐ray diffraction analysis validate machine hammer peening is a mechanical treatment without new compound generated. The friction test results in an enhancement in wear resistance of treated samples.

Hard rock fragmentation by dynamic conical pick indentation under confining pressure

Mechanical mining and excavation in deep metal mines can be regarded as the process of crushing hard rock by conical pick indentation. In this study, a confining pressure loading device was designed and used to carry out dynamic conical pick indentation crushing tests under confining pressure conditions on three types of granite with varying strengths, using the Split Hopkinson Pressure Bar (SHPB). The objective was to quantitatively investigate the effect of confining pressure and rock strength on the indentation crushing characteristics of deep hard rocks. The results indicate that as the confining pressure increases from 5 MPa to 20 MPa, the dimensional parameters such as volume, diameter and depth of the impact groove decrease linearly, while parameters such as the specific energy, indentation force, indentation index and energy utilization rate progressively increase. The increase in the confining pressure inhibits the formation of internal cracks in the rock, enhancing its resistance to pick indentation, which in turn makes rock fragmentation more difficult. This creates unfavorable conditions for efficient rock breaking. Furthermore, rock strength plays a crucial role in the pick indentation process. The higher the rock strength, the greater its resistance to pick indentation, leading to increased energy consumption, accelerated wear of the conical picks, and reduced efficiency in rock breaking.

Impact response of fractionally damped rectangular plates made of viscoelastic composite materials

The paper aims to find dynamic response of fractionally damped rectangular viscoelastic plates under low-velocity impact of a mass. The general fractional (Rubbery, Transition and Glassy) RTG model for the plate material was considered. First, the governing equation of the plate is derived and solved. Next, using the modified Hertz contact law, the governing integral equation of the problem in terms of indentation is derived and solved. Finally, relation between indentation and impact force is discretized and using the Mittag-Leffler function, history of impact force is obtained. The work is validated by comparison of the results with some particular cases and available experimental data.

Sticky feet: a tribological study of climbing shoe rubber

This study examines the tribological properties of climbing shoe rubbers, challenging the common belief in the climbing community that softer rubbers are inherently grippier. This study investigates the mechanical and wear characteristics of climbing shoe rubbers by employing a high-precision modular mechanical testing environment (Bruker UMT TriboLab) and representative granite counter-surfaces. Key parameters, including surface roughness, Shore A hardness, interfacial adhesion, static and dynamic friction coefficients, and material wear patterns, were analyzed. The mechanical properties of each rubber compound were characterized through Shore A hardness testing and ball indentation–retraction tests, measuring indentation force, energy, and adhesive properties. Sliding friction tests, simulating real climbing conditions, were conducted to understand the tribological behavior of each rubber compound under different loads, further analyzing static and dynamic friction coefficients and wear characteristics. The findings of this study indicate that rubber performance is a convolution of several factors, including material hardness, surface roughness, and interfacial adhesion. Contrary to popular belief, softer rubbers did not consistently exhibit superior tribological characteristics. The findings of this study suggest that climbing shoe selection and design should consider a broader range of material characteristics beyond hardness, emphasizing the role of surface roughness and adhesion in determining overall frictional performance. This research offers valuable insights for the climbing community, providing methodologies to benchmark climbing rubber material characteristics.

Axisymmetric Hertzian contact problem accounting for surface tension and strain gradient elasticity

In this paper, we investigate the axisymmetric Hertzian contact problem at micro-/nanoscale. The deformation of material bulk is described by a simplified theory of strain gradient elasticity, and the influence of surface tension is integrated based on the surface elasticity theory. Using the Mindlin's potential function method and double Fourier integral transform, the normal surface displacement induced by a concentrated force is derived in a closed form. Following this, the contact between a rigid sphere and an elastic half-space is formulated in terms of singular integral equation, which is numerically solved by applying the Gauss-Chebyshev method. The results indicate that the distribution of contact pressure is distinctly different from that in classical elasticity theory. The indented substrate tends to perform stiffer due to the effects of surface tension and strain gradient elasticity. When the contact radius is comparable with the material length parameter, the indentation force (depth) can be ten (three) times of that given by classical Hertz theory.

Unveiling Gating Behavior in Piezoionic Effect: toward Neuromimetic Tactile Sensing.

The human perception system's information processing is intricately linked to the nonlinear response and gating effect of neurons. While piezoionics holds potential in emulating the pressure sensing capability of biological skin, the incorporation of information processing functions seems neglected. Here, ionic gating behavior in piezoionic hydrogels is uncovered as a notable extension beyond the previously observed linear responses. The hydrogel can generate remarkably high voltages (700mV) and currents (7mA) when indentation forces surpass the threshold. Through a comprehensive analysis involving simulations and experimental investigations, it is proposed that the gating behavior emerges due to significant diffusion differences between cations and anions. To showcase the practical implications of this breakthrough, the piezoionic hydrogels are successfully integrated with prostheses and robot hands, demonstrating that the gating effect enables accurate discrimination between gentle and harsh touch. The advancement in neuromimetic tactile sensing has significant potential for emerging applications such as humanoid robotics and biomedical engineering, offering valuable opportunities for further development of embodied neuromorphic intelligence.

Effects of adhesive and frictional contacts on the nanoindentation of two-dimensional material drumheads

Nanoindentation of suspended circular thin films, dubbed drumhead nanoindentation, is a widely adopted technique for characterizing the mechanical properties of micro- or nano-membranes, including atomically thin two-dimensional (2D) materials. This method involves suspending an ultrathin specimen over a circular microhole and applying a precise indenting force at the center using an atomic force microscope (AFM) probe. Classical solutions assuming a point load and a fixed edge, which are referred to as Schwerin-type solutions, are commonly used to estimate Young’s modulus of the membrane material out of load–deflection measurements. However, given the widespread experimental evidence for adhesive and frictional contacts between the probe tip and the membrane, as well as sliding between the membrane and its supporting substrate, quantitative investigations of the effects of these interactions are required. In this paper, we formulate a boundary value problem to rigorously model such effects, ensuring relevance to experimental operations. Our numerical analyses reveal that the adhesive effect at the tip-membrane interface diminishes as the indentation depth increases or the tip size decreases. Furthermore, frictional interactions at this interface shift the maximum membrane stress from the center to the tip-membrane contact line with increasing indentation depth and interfacial shear stress. At large indentation depths, the size of the indenter tip and the sliding of the membrane-substrate are found to have a large effect on the indentation load–deflection relationship. Thus, we propose a new approximate formula for this relationship assuming a non-adhesive and frictionless spherical tip of a finite radius and a slippery contact with the supporting substrate. This formula is more accurate than the widely used Schwerin-type solution. It can be used to simultaneously extract the in-plane stiffness of the membrane and the shear strength at the membrane-substrate interface.

Investigating the influence of graphene coating thickness on Al0.3CoCrFeNi high-entropy alloy using molecular dynamics simulation

Graphene was proven to be an excellent surface-strengthening material. However, there needs to be more literature explaining its strengthening mechanism at the atomic level. This study systematically investigated the surface strengthening mechanism of graphene coating on the Al0.3CoCrFeNi high-entropy alloy (HEA) and the influence of loading-unloading cycles on the formation of internal defects in the material through molecular dynamics (MD) simulations at the atomic level. Research results show that the internal stress concentration in HEA without graphene coating leads to a more considerable residual depth after unloading. With the addition of a graphene coating, the material's stress area increases, effectively alleviating stress concentration and reducing residual depth. Furthermore, the lengths of Lomer-Cottrell dislocation locks and Hirth dislocation locks inside the material increase, enhancing the material's deformation resistance. The more layers of graphene, the larger the stress distribution area and the greater the hardness. Under the same indentation force, the number of HCP structures and amorphous structures inside the material is inversely proportional to the thickness of the graphene layers. In addition, after multiple loading and unloading cycles, the hardness of HEA/GP materials basically remains unchanged, while internal defects increase and residual depth increases.

Master Curves for Poroelastic Spherical Indentation With Step Displacement Loading

Abstract Theoretical and numerical analyses are conducted to rigorously construct master curves that can be used for interpretation of displacement-controlled poroelastic spherical indentation test. A fully coupled poroelastic solution is first derived within the framework of Biot’s theory using the McNamee–Gibson displacement function method. The fully saturated porous medium is assumed to consist of slightly compressible solid and fluid phases and the surface is assumed to be impermeable over the contact area and permeable everywhere else. In contrast to the cases in our previous studies with an either fully permeable or impermeable surface, the mixed drainage condition yields two coupled sets of dual integral equations instead of one in the Laplace transform domain. The theoretical solutions show that for this class of poroelastic spherical indentation problems, relaxation of the normalized indentation force is affected by material properties through weak dependence on a single-derived material constant only. Finite element analysis is then performed in order to examine the differences between the theoretical solution, obtained by imposing the normal displacement over the contact area, and the numerical results where frictionless contact between a rigid sphere and the poroelastic medium is explicitly modeled. A four-parameter elementary function, an approximation of the theoretical solution with its validity supported by the numerical analysis, is proposed as the master curve that can be conveniently used to aid the interpretation of the poroelastic spherical indentation test. Application of the master curve for the ramp-hold loading scenario is also discussed.

Synthesis and characterization of additively manufactured microcapsule‐reinforced polylactic acid composites for autonomous self‐healing

AbstractMaterial extrusion‐based additive manufacturing (AM) process builds the objects/structures through a precise feedstock deposition in a layer‐by‐layer manner. Polylactic acid (PLA) is a popular biodegradable feedstock in AM, while octyl methoxycinnamate (OMC) is known for its eco‐friendliness and ultraviolet (UV) protection properties. The present study focuses on the novel infusion methodology of OMC‐based microcapsules into PLA to develop self‐healing composite filaments. Post‐composition iterations, the optimum compositions for the filler and plasticizer were determined, and the filaments were extruded. Microcapsule‐infused PLA and the neat PLA samples were printed as per the American Society for Testing and Materials (ASTM) standard. The uniaxial tensile test results showed that the failure strain endured by the microcapsule‐infused samples was about 10 times more than the neat PLA counterparts. It is attributed to the effective load distribution and the complex polymerization reaction (due to the interaction of OMC with the matrix). Fracture surface morphology of the samples via optical microscopy (OM) and field emission scanning electron microscope (FESEM) affirmed the strong PLA‐OMC interface. A depreciation in the Brinell Hardness for the microcapsule‐based samples was due to the localized indenter force, causing greater damage in a narrow area than microcapsule ruptures' healing ability.Highlights The optimized composition of PLA: plasticizer:microcapsule is 1:0.04:0.05. Microcapsule‐infused PLA has improved Young's modulus and failure strain. Interaction with microcapsules improves elastic behavior and self‐healing. FESEM reveals close bonding of microcapsule with the PLA matrix.

Assessment of Intraday Variations in Skin Indentation Resistance.

Information about the mechanical properties of skin and their changes with age and other conditions is important to help characterize skin physiology and pathological changes. One method to obtain this information is to measure the force required to indent the skin to a specified indentation depth (FORCE). This process measures the tissue's resistance to indentation or its compressibility and is related to the tissue's elastic modulus. Since such measurements are made in clinical and other settings at various times of day (TOD), it is useful to estimate the extent of intraday variations in FORCE that may be expected. This report focuses on this issue. FORCE was self-measured on the volar forearm, 5 cm distal to the antecubital fossa, every two hours from 08:00 to 24:00 hours on two consecutive days by 12 medical students (six females and six males) who were trained in the measurement process using an indentation device (SkinFibroMeter). Variability in FORCE versus TOD was analyzed using the nonparametric Friedman test and differences between genders by the nonparametric Wilcoxon test. Differences between the first day (day 1) and the second day (day 2) were tested at each TOD. The whole-body fat percentage (FAT%) and water percentage (H2O%) were determined for each participant via bioimpedance measurements at 50 KHz. The age and BMI of the combined group (mean ± SD) were 24.5 ± 1.5 years and 23.2 ± 3.3 kg/m2.The overall average FORCE (mean ± SD) for the day over the 16 hours was 84.1 ± 22.7 mN and for day 2, it was 83.4 ± 28.5 mN with no significant difference between day 1 and day 2. For females, the overall two-day average FORCE (mean ± SD) over the 16 hours was 81.8 ± 20.3 mN and for males, it was 85.7 ± 30.1 mN with no significant difference between them (p = 0.271). Overall, there was no statistically significant difference in FORCE among TOD (p = 0.568). FORCE was not correlated with either FAT%, HTO%, or BMI. The findings indicate no statistically significant variation in indentation force in females, males, or combined concerning the TODof the measurement or differences between consecutive days at corresponding times. This suggests that whether such measurements are done in a research setting or within a clinic, they can be done at various TODwith minimal expected variation for a given subject. However, an extension of these findings to persons with skin conditions or ages not herein evaluated must await further study.

Uncovering Nanoindention Behavior of Amorphous/Crystalline High-Entropy-Alloy Composites.

Amorphous/crystalline high-entropy-alloy (HEA) composites show great promise as structural materials due to their exceptional mechanical properties. However, there is still a lack of understanding of the dynamic nanoindentation response of HEA composites at the atomic scale. Here, the mechanical behavior of amorphous/crystalline HEA composites under nanoindentation is investigated through a large-scale molecular dynamics simulation and a dislocation-based strength model, in terms of the indentation force, microstructural evolution, stress distribution, shear strain distribution, and surface topography. The results show that the uneven distribution of elements within the crystal leads to a strong heterogeneity of the surface tension during elastic deformation. The severe mismatch of the amorphous/crystalline interface combined with the rapid accumulation of elastic deformation energy causes a significant number of dislocation-based plastic deformation behaviors. The presence of surrounding dislocations inhibits the free slip of dislocations below the indenter, while the amorphous layer prevents the movement or disappearance of dislocations towards the substrate. A thin amorphous layer leads to great indentation force, and causes inconsistent stacking and movement patterns of surface atoms, resulting in local bulges and depressions at the macroscopic level. The increasing thickness of the amorphous layer hinders the extension of shear bands towards the lower part of the substrate. These findings shed light on the mechanical properties of amorphous/crystalline HEA composites and offer insights for the design of high-performance materials.

Contact fatigue of thin hard diamond-like carbon films on M50 steels under cyclic spherical micro-indentation

Contact fatigue behaviors of thin hard diamond-like carbon (DLC) films on M50 steels during cyclic spherical micro-indentations were investigated. The stress-strain evolution of the entire system was analyzed by finite element methods. The film fracture mechanisms and interfacial bearing responses under monotonic and repeated contacts were comprehensively explored. Concentrated tensile and shear stresses were found to, respectively, govern the initiation and propagation of the surface ring cracks. Elevated tensile stresses at the initiation and epilogue of each indentation cycle enhanced bottom radial cracking. At the interfaces, the maximum tensile (σnmax) and shear (σtmax) stresses occurred at the end of unloading and loading processes, respectively. With increasing maximum indentation forces, σnmax initially increased and then gradually decreased, while σtmax increased monotonically.

The effect of temperature on monocrystalline Si nanoindentation side effects: A molecular dynamics study

Monocrystalline Si materials has been widely used in the fields of micro-electro-mechanical systems and electronic chips. At the micro and nanoscale, there are differences in the mechanical properties at the workpiece side compared to its interior. Meanwhile, temperature also has a significant impact on the mechanical properties of materials. In this paper, to analyze the effect of the temperature on the nanoindentation side effect of monocrystalline Si, a series of molecular dynamics (MD) simulations of nanoindentation are performed under six different temperatures. The simulation results show that the plastic deformation behavior, indentation force, internal stress, and the Internal defects are closely related to the temperature in nanoindentation. This work attributes a better understanding of the temperature effect on the nanoindentation side effect of the monocrystalline Si materials.

Exploring the impact of pre-existing helium bubbles on nanoindentation in tungsten through molecular dynamics simulation

Gaining insight into the underlying mechanisms driving nanoindentation-induced behavior in tungsten is essential for comprehending its mechanical properties. Although the plasticity of conventional pure tungsten under nanocontact conditions is well understood, these theoretical constructs may become inadequate when applied to irradiated tungsten due to the interplay between helium bubbles and dislocations. Here, we employed an integrated approach, combining crystal defect theories, molecular dynamics simulations, and machine learning, to explore the initiation and progression of dislocations in tungsten containing helium bubbles during nanoindentation, focusing on elucidating the impact of helium bubbles. In contrast to the typical dislocation nucleation in pure tungsten, the presence of helium bubbles mitigates local shear strain, thereby hindering dislocation nucleation and propagation, leading to a reduction of indentation force. Additionally, we conducted a comparative analysis between samples with and without helium bubbles, examining factors such as atomic displacement, strain localization parameters, dislocation line length, and stress component distribution. More importantly, a significant outcome of our study is the establishment of a relationship between the consistent alteration in the shape of helium bubbles and their size during micro-scale nanoindentation, achieved through machine learning techniques. Our findings reveal that the area occupied by helium bubbles post-nanoindentation is inversely correlated with indentation depth and directly linked to helium bubble size. These discoveries represent a notable advancement in understanding the effects of irradiation to a certain degree.

Size Matters: Rethinking Hertz Model Interpretation for Cell Mechanics Using AFM.

Cell mechanics are a biophysical indicator of cell state, such as cancer metastasis, leukocyte activation, and cell cycle progression. Atomic force microscopy (AFM) is a widely used technique to measure cell mechanics, where the Young modulus of a cell is usually derived from the Hertz contact model. However, the Hertz model assumes that the cell is an elastic, isotropic, and homogeneous material and that the indentation is small compared to the cell size. These assumptions neglect the effects of the cytoskeleton, cell size and shape, and cell environment on cell deformation. In this study, we investigated the influence of cell size on the estimated Young's modulus using liposomes as cell models. Liposomes were prepared with different sizes and filled with phosphate buffered saline (PBS) or hyaluronic acid (HA) to mimic the cytoplasm. AFM was used to obtain the force indentation curves and fit them to the Hertz model. We found that the larger the liposome, the lower the estimated Young's modulus for both PBS-filled and HA-filled liposomes. This suggests that the Young modulus obtained from the Hertz model is not only a property of the cell material but also depends on the cell dimensions. Therefore, when comparing or interpreting cell mechanics using the Hertz model, it is essential to account for cell size.

Identification of dynamic coefficient matrix for drilling process simulations from measured tool geometry, axial force and torque

This paper aims to quantitatively analyze the relationship between forces acting on the tool tip and tool movement during drilling operations. The study encompasses axial and lateral vibrations superimposed on the nominal tool movement, arising from rigid body motion (rotational and axial velocities). Specifically, only forces attributed to the cutting process are considered, excluding considerations of indentation forces around the chisel edge. The research adopts a generalized approach, spanning from tool measurements to establishing the force model. The investigation involves measuring cutting forces and correlating them with the varying rake and inclination angles of the drill’s cutting edges. An analytical model is proposed to describe the distribution of all local force components along drill edges, considering the evolution of forces and geometry. The dynamic coefficient matrix is evaluated by using the identified cutting coefficient and tool geometry. Validation of the proposed methodology is demonstrated through drilling experiments on Ti6Al4V alloy, utilizing three solid carbide drills with distinct geometries. The proposed procedure allows complete identification of the dynamic characteristics from the measurements taken at the entrance stage of hole drilling operation. Moreover, the influence of tool geometry on cutting coefficients and dynamic coefficient matrices are discussed.

On the depth of cylindrical indentation of an elastic half-space for different types of displacement boundary conditions

Nonlinear relationships between the penetration depth δ and applied force F for cylindrical indentation of a half-space are derived corresponding to two types of displacement boundary conditions: (i) zero vertical displacement imposed at points x=±b of the free-surface of a half-space, and (ii) zero vertical displacement imposed at a point z=h below the indenter. The requirement that the work done by the indentation force must be equal to the work done by the contact pressure defines the minimum values of b and h for which the indentation is geometrically and physically possible. The minimum value of b is found to be about 10 times greater than the semi-width of the contact zone a=(4FR/πE∗)1/2, with the corresponding minimum value of the indentation depth δmin≈3.5δ0, where δ0=2F/πE∗ is the height of the contact zone under applied force F, and E∗=E/(1−ν2) is the plane strain elastic modulus. The minimum value of h is equal to about 21a in the case ν=1/3, and about 27a in the case ν=1/2. The relationship between h and b, corresponding to the same indentation depth δ≥δmin, is derived and shown to be nearly linear for large values of h/a and b/a. The obtained results are used to estimate the indentation depth of finite-size elastic bodies under different boundary constraints. Comparison with FEM prediction is made.

Machining mechanism and residual stress of AlCuCrFeNi alloy

This investigation utilizes molecular dynamics simulations to explore the mechanical response of the AlCuCrFeNi high-entropy alloy to nano-scraping employing an abrasive tip traversing the workpiece surface. This study investigates the influence of various parameters, such as grain size, pressing depth, alloy composition, temperature, and sliding distance, on plastic deformation, frictional behavior, dislocation density, wear mechanisms, and von Mises stress. The results reveal that increasing grain size leads to augmented force and hardness, indicative of a reverse Hall-Petch relationship. Moreover, scraping and indentation forces escalate with decreasing aluminum concentration and temperature. The analysis underscores the pivotal role of grain boundaries in impeding stress and strain propagation. Stress and strain concentrations are particularly evident at the interface between the scraping tool and the substrate and near the grain boundaries. Grain boundary slipping, bending, and grain merging are pivotal mechanisms contributing to the distortion of polycrystalline materials, culminating in solid dislocations within grain boundaries. Furthermore, heightened compression depth and sliding distance exacerbate plastic deformation and subsurface damage. Notably, the presence of copper atoms enhances the HEA's resistance to deformation. This research enhances comprehension of the nano-scraping behavior and deformation mechanisms in AlCuCrFeNi HEA during ultra-precision processing.