Indentation Velocity Research Articles

Analysis of bi-directional functionally graded plate on an elastic foundation subjected to low velocity impact using the refined plate theory

This study investigates the mechanical response of a bi-directional functionally graded plate consisting of three distinct materials when subjected to low-velocity impact. Utilizing the New Refined Plate Theory, the research explores the mechanical behavior of the plate resting on a Pasternak elastic foundation, providing insights useful for engineering applications. The investigation examines various parameters, including initial impact velocity, projectile radius, volume fraction indices, and elastic foundation stiffness, and their effects on critical response characteristics such as contact force, indentation, lateral deflection, and projectile velocity. The theoretical predictions are validated through detailed comparisons with existing literature and numerical simulations, ensuring the reliability and applicability of the proposed methodology. This study introduces a novel approach using refined plate theory to analyze low-velocity impact on 2D-FGMs, providing practical insights for structural analysis. The findings deepen understanding of functionally graded materials and enhance the evaluation of impact-resistant structures. The research highlights the importance of diverse parameters in improving structural performance and reliability, relevant across aerospace, civil, and mechanical engineering. Detailed exploration shows that initial impact velocities and projectile radius enhance impact force and deflection, while volume fraction indices and foundation stiffness influence the dynamic response.

Micromechanical response of graphene coating on nt-TiAl under nanoindentation

The nanoindentation response of graphene (Gr) coating on nanotwin titanium-aluminum (nt-TiAl) matrix composites was studied using molecular dynamics (MD) simulation. The indentation velocity, twin boundary spacing, and parallel and vertical Z-axes are studied. The results show that the bearing capacity and hardness of Gr coating is significantly higher than that after coating failure, and the load-displacement curve shows the same phenomenon. Damage to the substrate material at varying speeds is indicated by atomic aggregation near the Gr coating, with the center of aggregation showing a negative correlation with indentation velocity. The matrix's damaged area is larger when the twin layer is perpendicular to the Z-axis and deeper when parallel, showing that the twin structure limits material damage by hindering dislocation expansion. Moreover, the presence of Gr coating delayed the matrix's plastic deformation process. This delay effect significantly improves the mechanical properties of composites, which have potential applications in aerospace.

Atomistic insight of deformation mechanisms and mechanical characteristics of nano-scale silver (100) using nanoindentation

This work aims to utilize the widely adopted nanoindentation technique to explore the deformation behavior and mechanical characteristics of nanocrystalline silver (Ag) materials. Molecular Dynamics simulations were conducted to understand the material behavior at the nanometer scale. In this simulation, the effect of indentation velocity and indentation depth on defect formation and hardness during nanoindentation of Ag specimens was analyzed and discussed in detail. The results show that the deformation behavior of the Ag specimen was affected by different indentation velocities. These phenomena were confirmed by analyzing the load-displacement curve, which indicates elastic deformation by the appearance of a linear load-displacement at low indentation velocities. In contrast, plastic deformation was found by the presence of intensified serration in the load-displacement relationship at higher indentation velocities. In these cases, the hardness showed little variation when the indenter velocity was increased from 5 m/s to 10 m/s, whereas a significant increase in hardness was observed when the indentation velocity was further increased to 20 m/s. Importantly, the progression of load-displacement curves during nanoindentation demonstrates the occurrence of minor and major load drops, corresponding to an increase in indentation depth from 0.5 nm to 2 nm respectively. These findings were elucidated through dislocation extraction analysis (DXA), which revealed that a minor load drop at low indentation depths is attributed to the nucleation of an amorphous structure, while a major load drop at higher indentation depths is associated with the expansion of dislocation nucleation. Consequently, the hardness increased significantly as the indentation depth increased. This research, provides insight into atomistic investigation and offers guidelines for designing materials with excellent mechanical properties using nanoindentation.

Numerical modeling of flax-woven reinforced composites submitted to quasi-static indentation and low velocity impact

Numerical modeling of flax-woven reinforced composites submitted to quasi-static indentation and low velocity impact

Atomistic simulation of nanoindentation behavior of amorphous/crystalline dual-phase high entropy alloys

High-entropy alloys (HEAs) are a new type of multi-principal metal materials that exhibit excellent mechanical properties. However, the strength–ductility balance in the HEAs remains a challenge that needs to be addressed. The amorphous/crystalline (A/C) structure is a new design strategy to achieve high strength and excellent ductility of the HEAs. Here, the influences of amorphous layer spacing, indenter velocity, and indenter radius on the mechanical properties and microstructure evolution of the A/C dual-phase CoCrFeMnNi HEAs under nanoindentation were investigated by molecular dynamics (MD) simulation. The results indicate that the plastic deformation mechanism of the monocrystalline HEAs is mainly dominated by the nucleation and slip of dislocations, while the plastic deformation mechanism of the dual-phase HEAs is mainly dominated by the interaction between dislocations and amorphous phases. The results show that the average indentation force of the dual-phase HEAs increases with the increase of the amorphous layer spacing. The amorphous layer in the HEAs can hinder the expansion of dislocations, limiting them to the crystalline matrix between the two amorphous layers. The results also indicate that Young's modulus of the HEAs increases with the increase of the indentation velocity and indentation radius. However, the hardness of HEAs is positively correlated with the indenter velocity, and negatively correlated with the indenter radius. It should be noted that the critical indentation depth and critical indentation force for the plastic deformation of the dual-phase HEAs decrease with the increase of indenter velocity, which is opposite to that of the single-phase crystalline HEAs.

Rate-independent hysteretic energy dissipation in collagen fibrils.

Nanoindentation cycles measured with an atomic force microscope on hydrated collagen fibrils exhibit a rate-independent hysteresis with return point memory. This previously unknown energy dissipation mechanism describes in unified form elastoplastic indentation, capillary adhesion, and surface leveling at indentation velocities smaller than 1 μm s-1, where viscous friction is negligible. A generic hysteresis model, based on force-distance data measured during one large approach-retract cycle, predicts the force (output) and the dissipated energy for arbitrary indentation trajectories (input). While both quantities are rate independent, they do depend nonlinearly on indentation history and on indentation amplitude.

Impact resistance and damage mechanism of polyurea coated CFRP laminates under quasi-static indentation and low velocity impact

In this study, polyurea coating has been applied to improve the impact resistance of carbon fiber reinforced plastics (CFRP) battery pack housing under automotive crash condition. The quasi-static indentation test and low velocity impact test were carried out to study the impact response of polyurea coated unidirectional and plain woven CFRP laminates with three coating methods. The impact velocity was selected from 10−4 m/s to 4.5 m/s. In addition, damage mechanism and failure modes of the laminates were analyzed, focusing on the identification of dominant damage modes and crack evolution. It was demonstrated that thin polyurea coating can improve the impact resistance of both unidirectional and plain woven CFRP, while the former was more significant than the latter. The specific energy absorption had 94% and 51% increment under low velocity impact and quasi-static indentation. The front coating method was the best polyurea coating method. Results also revealed that the polyurea coating increased the damage area and fracture crack of polyurea coated CFRP laminates with different damage mechanisms. This study confirms that the use of polyurea coated CFRP laminates is an interesting and promising structure candidate for crash safety design and lightweight design of battery pack housing.

Effects of Holding Time and Temperature of Creasing Knife on Crease Bending Characteristics of Milk Carton Subjected to Indentation of Flat-Edge Creasing Knife

Since the material properties of paperboard depend on the processing strain rate and the temperature elevation of the paperboard, the mechanical conditions of the scoring tool (creasing knife) are important for precisely and stably folding the scored zone of the paperboard. When the temperature and the indentation velocity of the creasing knife are changed irregularly during the scoring process, the permanent-indented (residually scored) depth of the paperboard seems to be affected by the temperature and the indentation time of the creasing knife. Although the temperature-dependent and time-dependent behavior of several thin paperboards have been known in the past, their combined behavior was not sufficiently discussed regarding the crease bending characteristics of the paperboard. In this work, the time-dependent and temperature-dependent scoring, and the corresponded bending characteristics of liquid-container-purpose paperboard of basis weight 313g/m2 (thickness of t = 0.47mm) were experimentally investigated using a bending (folding) tester, when varying the holding time and the temperature of a flat-edge creasing knife at two levels of the normalized indentation depth d/t = 0.68 and 1.02. As the results, the first peak bending moment Mp1, the first stiffness C1 (the gradient of bending moment resistance by the folding angle at an angle of 0—4 degrees), and the rating bending moment resistance at the right-angle M90,1(0) were characterized with the holding time and the temperature elevation of the creasing knife at the pre-stage (scoring) process. Also, some explicit expressions of C1, Mp1, M90,1(0) with the permanent scored depth were revealed as a static relationship. It is concluded that the temperature variation and the holding time of the creasing knife are important parameters which must be controlled in the manufacturing process of liquid package.

Inertial effect on dynamic hardness and apparent strain-rate sensitivity of ductile materials

Indentation is a simple and one of the oldest small-scale test methods for characterizing the mechanical response of materials. Recently, there has been a growing interest in dynamic indentation due to its potential to characterize the mechanical response of small volume of materials at high strain-rates. Herein, we focus on understanding the synergistic effects of materials’ inherent strain-rate sensitivity and inertia on the scaling of dynamic hardness with indentation strain-rate. Specifically, we analyze the dynamic indentation response of ductile materials over a wide range of indentation velocities, utilizing both finite element calculations and an analytical cavity expansion model. The materials are assumed to follow isotropic elastic–viscoplastic constitutive relations, with the viscoplastic part described by either an overstress or a simple power-law model. Our results show that below a critical indentation strain-rate, the scaling of dynamic hardness with indentation strain-rate is the same as the viscoplastic constitutive description. Therefore, at these strain-rates, dynamic hardness can effectively characterize a material’s strain-rate sensitivity, provided its viscoplastic constitutive description is known beforehand. However, above the critical indentation strain-rate, the dynamic hardness increases rapidly with indentation strain-rate. This phenomenon indicates an apparent strain-rate sensitivity that exceeds the expected response of the viscoplastic constitutive description. Moreover, above the critical indentation strain-rate, the indentation depth acts as a natural length-scale, with higher hardness observed at greater depths due to increased inertial effects. In other words, above the critical indentation strain-rate, dynamic hardness cannot be taken as an intrinsic material property.

Faster Indentation Influences Skin Deformation To Reduce Tactile Discriminability of Compliant Objects.

To discriminate the compliance of soft objects, we rely upon spatiotemporal cues in the mechanical deformation of the skin. However, we have few direct observations of skin deformation over time, in particular how its response differs with indentation velocities and depths, and thereby helps inform our perceptual judgments. To help fill this gap, we develop a 3D stereo imaging method to observe contact of the skin's surface with transparent, compliant stimuli. Experiments with human-subjects, in passive touch, are conducted with stimuli varying in compliance, indentation depth, velocity, and time duration. The results indicate that contact durations greater than 0.4 s are perceptually discriminable. Moreover, compliant pairs delivered at higher velocities are more difficult to discriminate because they induce smaller differences in deformation. In a detailed quantification of the skin's surface deformation, we find that several, independent cues aid perception. In particular, the rate of change of gross contact area best correlates with discriminability, across indentation velocities and compliances. However, cues associated with skin surface curvature and bulk force are also predictive, for stimuli more and less compliant than skin, respectively. These findings and detailed measurements seek to inform the design of haptic interfaces.

Simulation and dimensional analysis of instrumented dynamic spherical indentation of ductile metals

Finite element (FE) modeling of instrumented dynamic indentation experiments in a miniature Kolsky bar is undertaken. Geometry, including an output bar with machined spherical indenter tip, and velocity history boundary conditions are extracted directly from experimental diagnostics. The test material (i.e., substrate) is polycrystalline aluminum alloy Al 6061-T6. The constitutive model used in simulations accounts for isotropic elasticity and isotropic plasticity with strain hardening, strain-rate hardening, and thermal softening under adiabatic conditions. The FE model, with representative material parameters culled from the literature, accurately reproduces the curvature of the experimental load versus depth data for three different experimental indentation velocity histories. A framework for dimensional analysis of instrumented dynamic spherical indentation is set forth, improving upon prior work. Parametric FE simulations reveal sensitivity, or lack thereof, of the predicted response to variations in the proposed independent dimensionless variables encompassing material properties. For the indenter size, maximum depth, and maximum strain rate imposed experimentally on the order of 103/s, force-depth predictions are nearly unaffected by realistic variations in mass density, melting temperature, and thermal softening parameters when the sample is initially at room temperature. Predictions are affected by elastic constants (the elastic modulus and to a lesser extent, Poisson’s ratio), initial yield strength, two strain hardening parameters, and strain rate sensitivity. Predictions are also notably affected by initial temperature, with thermal softening prominent at high enough initial temperature or much higher loading rates. Based on the dimensional analysis, static indentation and elevated temperature indentation experiments are proposed for extraction of quasi-static and thermal material properties from previously uncharacterized metals, and dynamic indentation is proposed for extraction of rate sensitivity that cannot be obtained from static tests. Rate sensitivity obtained in this way from the novel instrumented dynamic spherical indentation experiments and FE simulations produces a parameterized stress–strain response for Al 6061-T6 reasonably validated by external studies for strain rates up to the order of 103/s.

Low-velocity impact, buckling, and vibrations of the piezoelectric doubly curved system via coupled Galerkin and Newmark method

ABSTRACT In the present study, buckling and vibrational analysis of a double-curved piezoelectric panel structure under low-velocity impact force is presented. In this regard, the first-order deformation theory of shell structures is utilized to approximate the displacement of the shell, and the linear strain-displacement relations are presented in a constitutive equation in small deformation elastic region. Finally, the principle of virtual work is exploited to obtain equations of motion under electrical and mechanical loads. The complexity of the equations of double-curved shell structure under electrical and impact loads necessitates using semi-analytical methods in obtaining the effects of different factors on the frequency, contact force, and indentation of the impactor. The results are presented in a detailed parametric study. Effects of moduli of elasticity of both panel and impactor on the contact force and indenter velocity are investigated. As a desirable result, it is determined that in a certain range of applied external voltage, the vibration of the panel is suppressed completely.

Nanoindentation characteristics of nanocrystalline tungsten via atomistic simulation

ABSTRACT Molecular dynamics simulations are performed to explore nanoindentation characteristics of tungsten, and the influences of grain size, indenter velocity, indenter size, and temperature are discussed. The results illustrate that the hardness reduces as the grain size (5.00 ∼ 24.62 nm) decreases. There is no phase change observed during the whole deformation process. For monocrystalline W, the dislocation nucleation and propagation dominate the deformation mechanisms. Differently, the primary deformation mode of nanocrystalline W is the grain split and motion of GBs. Dislocations primarily nucleate below the contact surface of the indenter and substrate and then glide in the grain core. The monocrystalline W has better pattern-forming ability than nanocrystalline. Besides, the pattern-forming ability of nanocrystalline W is negatively correlated with the average grain size (5.00 ∼ 24.62 nm). The von Mises stress is mainly concentrated in the interface between the indenter and substrate, the dislocation area for monocrystalline, and grain boundaries for nanocrystalline. The indentation force and hardness are positively correlated with indenter radius size (30 ∼ 80 Å), negatively correlated with temperature (10 ∼ 1500 K), and insensitive to the indenter velocity when velocity is lower than 3.0 Å /ps (300 m/s).

On energy absorption and low-velocity impact response of functionally graded graphene oxide powders-reinforced nanocomposite panel on the viscoelastic substrate

Curved panels are used for ships due to complex situations that can be under external loading. So, it is very important to know about the stability related to the curved system under Low-Velocity Impact (LVI). To improve the stability of this kind of structure, graphene oxide powders (GOPs) are added to its matrix. In addition, the contact force between the impactor and shell is evaluated by implementing Hertz contact theory. So, in the current work, as a first attempt, energy absorption and low-velocity impact response of functionally graded graphene oxide powders-reinforced nanocomposite panel on the viscoelastic substrate is presented. Higher-order shear deformation theory (HSDT), which has twelve factors, is employed to determine the displacement domains. Also, the minimum potential energy technique is designated to obtain the governing equations and end conditions. Moreover, Galerkin and Newmark methods are chosen to solve the relationships. The governing equations related to the curved system under external excitation aimed at achieving the LVI and dynamic outputs are determined by the connection of Galerkin and Newmark methods. The uniqueness of this research is considering the impacts associated with HSDT and various Boundary Conditions (BCs) in addition to considering FG oxide powder reinforcement. The outputs segment displays the effects related to the BCs, the radius of the impactor, mass, and velocity, as well as the weight fraction related to the GOPs on contact force, the indentation, and the indenter velocity.

Vibration–impact study on the functionally graded graphene nanoplatelets reinforced composite curved open-type shell

This paper investigates the stability of the curved system reinforced by graphene nanoplatelets (GPLs) under low-velocity impact. Hertz contact theory is employed in order to model the contact force between the shell and the impactor. In order to acquire the displacement domains, higher-order shear deformation theory (HSDT) with twelve parameters is used. The governing equations, in addition to end conditions, are attained by the Minimum potential energy method. Then the formulations are solved through the Galerkin method as well as the Newmark method. By coupling Galerkin and Newmark methods, we solved the governing equations of the curved system under external excitation for attaining the dynamic and low-velocity impact responses. The results section shows the influence of boundary conditions, velocity, mass, and radius of the impactor, and the weight fraction of GPLs on indenter velocity, contact force, and the indentation of the GPLs reinforced open-type shell under low-velocity impact.

Structural response of sandwich structures with CFRP face sheets under quasi-static indentation and high velocity impact: An experimental and numerical study

Honeycomb sandwich structures (HSSs) with carbon fibre reinforced polymer (CFRP) composite face sheets are extensively used as light-weight structures in aerospace engineering due to their high strength-to-weight ratio and energy absorption properties. However, the composite face sheets are highly vulnerable to impact loads and cause damage to the structure based on the impact energy. This study investigates the structural response of HSS with CFRP face sheets under quasi-static indentation and a wide range of impact energy: low to high velocity impact. A finite-element model was developed and numerical simulations were carried out at various impact energies, thereby providing deeper insights into the impact dynamics and understanding various damage states such as dent, front face sheet perforation, core damage and rear face sheet penetration. The numerical simulation result was compared with the experimentally tested HSS using a single-stage gas gun under 53.6 J to validate the finite-element model in terms of deformation and damage status. A quasi-static indentation test was conducted and numerically predicted force data under impact test for the complete perforation case was compared to address the dependency of rate of loading. The carbon nanotube (CNT) with various weight percentages (wt%), such as 0.2, 0.4 and 0.6, was added to the matrix system through a vacuum assisted resin transfer technique and experiments were conducted at 79, 107 and 135 J. The impact resistance increases with CNT addition and hence no perforation was recorded for all the test cases of 0.6 wt% CNT addition. The influence of CNT addition on the damage area is more on the bottom face sheet and a 57% reduction in damage area was recorded for the case of 0.6 wt% CNT addition at 135 J impact energy when compared to the neat carbon/epoxy composite.

The Influence of Electrode Indentation Rate on LME Formation during RSW

During resistance spot welding of zinc-coated advanced high-strength steels (AHSSs) for automotive production, liquid metal embrittlement (LME) cracking may occur in the event of a combination of various unfavorable influences. In this study, the interactions of different welding current levels and weld times on the tendency for LME cracking in third-generation AHSSs were investigated. LME manifested itself as high-penetration cracks around the circumference of the spot welds for welding currents closely below the expulsion limit. At the same time, the observed tendency for LME cracking showed no direct correlation with the overall heat input of the investigated welding processes. To identify a reliable indicator of the tendency for LME cracking, the local strain rate at the origin of the observed cracks was analyzed over the course of the welding process via finite element simulation. While the local strain rate showed a good correlation with the process-specific LME cracking tendency, it was difficult to interpret due to its discontinuous course. Therefore, based on the experimental measurement of electrode displacement during welding, electrode indentation velocity was proposed as a descriptive indicator for quantifying cracking tendency.

Pseudo-shakedown of rectangular plates under repeated impacts

The pseudo-shakedown phenomenon for rectangular plates subjected to repeated impacts is studied using a numerical simulation method. The wide applicability of the finite element modelling techniques for repeated impacts is validated against reported experimental results on different structural components. The dynamic response of the plates, such as the plate displacement, impact force, indenter velocity, and absorbed energy, among other parameters, are presented in detail and analysed. The analysis provides a deep insight into the pseudo-shakedown behaviour of elastoplastic plates under repeated impacts. A criterion based on the critical displacement is drawn for the pseudo-shakedown occurrence. The concept of two displacements, i.e. ‘necking displacement’ and ‘failure displacement’ is proposed, from which some mechanical characteristics of structures under low velocity repeated impacts are revealed and clarified. The proposed two displacements are useful tools to estimate the occurrence of pseudo-shakedown and structural failure.

Molecular Dynamics Simulations of Nanoindentation of CuNi Alloy

In this paper, molecular dynamics was used to simulate the indentation process of copper–nickel (CuNi) alloy. Its mechanical properties and behaviors were investigated focusing on factors such as indentation velocity, test temperature and crystal orientation. Generally speaking, dislocation generations and slips, stacking faults, extended dislocations and deformation twins, one or more of them come into play the dominant role during plastic deformation, which in return leads to an improved or reduced hardness of CuNi alloy. Specifically, simulations and analyses reveal the following: (1) its hardness [Formula: see text] increases with [Formula: see text] increasing, but the reduced elastic modulus [Formula: see text] is not sensitive to [Formula: see text]; when it comes to test temperature [Formula: see text], both [Formula: see text] and [Formula: see text] are reduced at elevated [Formula: see text]; besides, the CuNi alloy along [Formula: see text] owns the highest [Formula: see text] and [Formula: see text], the value of [Formula: see text] along [Formula: see text] is slightly smaller than that along [Formula: see text] (2) the dislocation density [Formula: see text] varies severely in the early stage of indentation and then generally levels off when indentation depth reaches approximately 1.5[Formula: see text]nm; by and large, its hardness and dislocation density follow the classical Taylor hardening model and the hardening coefficient does depend on the three factors; (3) the plastic-zone size parameter [Formula: see text], when [Formula: see text] or equivalently [Formula: see text] can be taken as constant roughly 4.0 except in the case of indentation along [Formula: see text], in which it is about 5.7.

Numerical simulation of deformation and fracture processes during static and dynamic perforation of thin plates from high-strength materials

The paper presents the calculation technique for static and dynamic perforation of thin high-strength steel plates using different models of material deformation and fracture. The calculations have been performed employing the finite element (FE) method and Johnson-Cook material deformation model. The material parameters are specified for Armox 500T steel. The influence of the indenter shape, loading rate, and contact conditions on the material deformation and fracture is investigated. The distribution fields of strains and stresses at different time points are constructed. The variation in the indenter velocity during the perforation of the plates is determined, and the change in the strain rate of the fracture zone is estimated. The obtained results are used to develop the techniques for testing high-strength steels under static and dynamic perforation. The comparison of the results of experiments and calculations will help to specify the values of the material models’ parameters for modeling high-speed penetration processes.