Indentation Stress Field Research Articles

Effect of Forge-Time on Electrode Indentation, Thermal and Residual Stress Fields in Resistance Spot Weld Joints of AISI 1008 Steel Sheets

Effect of Forge-Time on Electrode Indentation, Thermal and Residual Stress Fields in Resistance Spot Weld Joints of AISI 1008 Steel Sheets

Influence of pre-existing configurations of dislocations on the initial pop-in load during nanoindentation in a CrCoNi medium-entropy alloy

ABSTRACT The origin and mechanisms responsible for incipient plasticity in metals are still poorly understood. Moreover, the reasons for the recently reported large scattering of the initial pop-in load remain unclear. Hence, this study addresses these issues through a combination of nanoindentation tests and electron channelling contrast imaging characterisation considering a CrCoNi medium-entropy alloy. Experimental findings were also supported by elastic calculations that consider both the indentation and dislocation stress fields. A wide scatter in the maximum shear stress underneath the indenter, as expected, was observed for the analysis based on dislocation density. As a consequence, the spatial arrangement of dislocations within the indented region or local dislocation configuration is introduced as a new parameter to overcome overly simple analysis based on the dislocation density. The maximum shear stress underneath the indenter increased from 6 GPa for dislocation closer to the indentation axis to 11 GPa at 600 nm for dislocation far away from it. Additionally, elastic calculations revealed that the response to the incoming nanoindenter was different for dislocations with different configurations. Thus, the complex interactions of stress fields due to configurations of dislocations and indentation account for the large scatter of the maximum shear stress beneath the indenter.

Densification effects on the fracture in fused silica under Vickers indentation

This study investigates the effects of densification on the deformation and fracture in fused silica under Vickers indentation by both the finite element analysis (FEA) and experimental tests. A refined elliptical constitutive model was used, which enables us to investigate the effects of the evolution of yield stress under pure shear and elastic properties with densification. The densification distribution was predicted and compared with experiments. The plastic deformation and indentation stress fields were used to analyze the initiation and morphology of various crack types. The formation mechanism of borderline cracks was revealed for the first time. This study reveals that the asymmetry of the densification distribution and elastic-plastic boundary significantly influences the cracking behavior. Under the Vickers indentation, conical cracks have the largest penetration depth. When these cracks emerge from a region far from the impression, they extend with constant radii to form circles on the sample surface. Otherwise, they tend to be initiated at the centers of the indenter-material contact edges before propagating towards the impression corners with increasing radii. Therefore, the borderline cracks consisting of successive partial conical cracks can form at a low load and makes them the first type of crack to appear.

Radial cracking at Vickers indentations in pristine flat/square silica fibers

AbstractIt has been found that the pristine surface of as‐drawn, flat silica fibers can be indented in air (~50%RH) using a Vickers diamond at a load of 11N without severe cracking during loading. Cracking does occur during unloading, but rather than ring and cone cracks as has been found by many others, radial cracks are observed: essentially as found in “normal” silicate glasses. This normal type cracking in silica glass has been also observed in detail at a high magnification by using a self‐made indentation microscope. It is suggested that the ring/cone cracks usually seen in a silica glass plate are the result of the propagation of the flaws normally present on surface, that is, “pre‐existing cracks.” The data are discussed using Yoffe's model which represents the indentation stress field.

Sharp indentation stress fields in fused silica: Finite element analysis and Yoffe analytic model

AbstractThe closed‐form Yoffe analytic model (1982), which superimposes two linear‐elastic stress fields, was developed as a first approximation to quantify the mechanical response of silicate glasses to sharp indentation. However, a detailed study with both experimental validation and numerical verification has yet to be published. This paper presents such a study, wherein experimental observation of crack systems in fused silica and numerical results from finite element analysis (FEA) are used to demonstrate the limitations of this analytic superimposition model. Specifically, analytic stress fields deviate from FEA numerical results and are inconsistent with several commonly observed crack systems. In contrast, FEA generated stress fields are entirely consistent with experimentally observed crack systems. Upon further investigation, it was found that the analytic model, with one tunable parameter, could not be adjusted to correlate with FEA and experimental evidence.

A finite element study on the effects of densification on fused silica under indentation

The pressure-induced densification significantly affects the deformation and damage behavior of fused silica. This paper presents a finite element analysis (FEA) of the densification and its effects on the deformation in fused silica under indentation. An elliptical constitutive model was refined to consider the influence of densification on elastic properties and its saturation with hydrostatic pressure. By matching the simulated indentation hardness to experiments, the plastic properties of fused silica were more accurately identified. FEA shows that the modified elliptical model can improve the prediction accuracy of the load-displacement curve of Berkovich indentation. As a widely-used reference material, the heavy densification in fused silica dose not influence the calibration accuracy of the tip area function in the Oliver-Pharr method, which provides a theoretical foundation for the use of fused silica as a reference material. With the modified elliptical model, the FEA successfully predicted the geometry of plastic zone, and the extent of elastic recovery and densification, which provided input parameters for the analytical embedded center of dilation (ECD) model of indentation stress field. Results show that the stress fields under a conical indenter predicted by the FEA agreed well with the ECD model.

In-situ observation of the initiation of plasticity by nucleation of prismatic dislocation loops

The elastic-to-plastic transition during the deformation of a dislocation-free nanoscale volume is accompanied by displacement bursts associated with dislocation nucleation. The dislocations that nucleate during the so-called “pop-in” burst take the form of prismatic dislocation loops (PDLs) and exhibit characteristic burst-like emission and plastic recovery. Here, we report the in-situ transmission electron microscopy (TEM) observation of the initial plasticity ensued by burst-like emission of PDLs on nanoindentation of dislocation-free Au nanowires. The in-situ TEM nanoindentation showed that the nucleation and subsequent cross slip of shear loop(s) are the rate-limiting steps. As the indentation size increases, the cross slip of shear loop becomes favored, resulting in a transition from PDLs to open half-loops to helical dislocations. In the present case of nanoindentation of dislocation-free volumes, the PDLs glide out of the indentation stress field while spreading the plastic zone, as opposed to the underlying assumption of the Nix-Gao model.

Weakly anisotropic residual contact stress in silicon demonstrated by electron backscatter diffraction and expanding cavity models

The residual stress field surrounding an elastic-plastic spherical indentation contact in Si is determined by electron backscatter diffraction (EBSD)-based experimental measurements and expanding hemispherical cavity-based models. The experiments provide support for indentations as test vehicles for assessment of EBSD as a two-dimensional deformation mapping method but make clear that selection of coordinate axes is critical to determining the correct representation of a stress field. The use of principal stress coordinates rather than the conventional Cartesian coordinates is required in cases in which the direction of the stress field is not aligned with Cartesian axes. In particular, the use of principal coordinates in the analysis of a spherical indentation stress field in Si removed misleading artefacts from the Cartesian-based field and revealed only a weak effect of Si crystalline elastic anisotropy. The experimental results are supported by isotropic and anisotropic finite element analysis models.

Estimation of peening effects of random and regular peening patterns

Shot peening and peen forming are respectively used to strengthen and form a component by blasting numerous shots on the component. A large number of analytical and numerical researches have focused on revealing the effects of various peening parameters. The shot impacting positions are usually supposed as a regular or random distribution, but there is a lack of intermediate measurand to connect the regular and random peening effects. This paper is aimed to estimate the peening effects of different peening patterns with different measurands, such as peening coverage and impacting density. Two types of 3D finite element (FE) models with regularly and randomly distributed shots are developed with dynamic-implicit solver of Abaqus. A theoretical equation for calculating random peening coverage is developed to calculate the coverage within an area with symmetry boundaries. The simulation results reveal the evolutions of indentation size, peening coverage and stress field. The equivalent forces on the cross section of plate corresponding to the induced stresses of regular and random peening are compared under the same coverage and impacting density respectively. Peen forming experiments with strict boundary constraints are performed to verify the simulation methods and agreement is observed.

Temperature dependence of indentation size effect, dislocation pile‐ups, and lattice friction in (001) strontium titanate

AbstractNanoindentations with a Berkovich type indenter were performed on (001) strontium titanate (STO) single crystal at 25°C and 350°C, analyzing the influence of temperature on the indentation size effect (ISE) and dislocation structure around the residual impression. It is found that the STO exhibits an ISE, which is strongly reduced at 350°C compared to 25°C. The dislocation structure around the residual impression has been resolved using an etch‐pit technique. At 25°C, the extension of the dislocation pile‐ups were found to be shorter as compared to 350°C. This also correlates with the smaller size effects at 350°C. Peach‐Koehler forces and the elastic‐plastic indentation stress field were used to model the influence of the lattice frictional stress on the dislocation pile‐ups. Based on an equilibrium position of the outermost dislocations, the average lattice frictional stresses were calculated to be 89 MPa and 46 MPa at 25°C and 350°C, respectively.

XFEM investigation on Knoop indentation cracking: Fracture toughness and aspect-ratio of radial-median cracks

In sharp indentation of brittle materials, cracks form below the impression or at its corners and propagate further during unloading. The dimensions of radial-median cracks can be exploited to derive the fracture toughness. Knoop indentation has the merit that only one large crack is produced. This and the shallow plastic zone make it the preferred method for crack growth experiments, but which require information on the initial crack shape. For investigation of the complex indentation stress field, which is moreover perturbed by cracking, the extended finite element method (XFEM) is an ideal tool. Results show that the point load assumption holds for sufficient loading, which means that Knoop indentation can be used for fracture toughness evaluation. During loading the plastic zone evolves linearly with depth h, while crack depth cz is found to evolve according to h ∝ cz3/4. For well-developed cracks, the crack aspect-ratio ρ ≡ cz/c (c is the length of the crack on the surface) is load-independent. The XFE model is validated through comparison with experimental results from the literature. Based on parameter studies, we establish functions that allow determination of fracture toughness and crack aspect-ratio. It is demonstrated that the mapping functions work well.

Formation of extended prismatic dislocation structures under indentation

Prismatic dislocation structures are often observed after indentation experiments. These structures usually start from the zone of high dislocation density underneath an indenter tip, but extend far beyond. Three dimensional Discrete Dislocation Dynamics simulations show how these complex structures can be formed from preexisting dislocations. The specifics of the indentation stress field and the crystallographic orientation play an important role for the formation of these structures. The mechanism of formation of the prismatic dislocations loops is dominated by stress controlled cross slip events, with cross slip locations reflecting the symmetry of the indentation stress field.

Fracture-based model of periodic-arrayed indentation for rock cutting

Periodic singular stress fields and K-dominant regions arise adjacent to sharp 90° indenter edges if an elastic substrate is subject to indentation with rigid, flat-ended and periodic indenters. The concept of indentation stress intensity factor Kind is convenient to describe such a singular indentation stress field, which is mathematically similar to that of a Mode-I crack. The singular indentation stress field is sufficient to induce surface cracking even if the substrate surface is free of any micro-cracks. This surface cracking mechanism generated from the flat-ended indentation potentially can play a significant role in damage analysis of rock cutting. During the rock-cutting processing, those periodic singular-stress fields will move along the rock surface, leading to continuous rock surface fracture. In this study, a fracture mechanics model is proposed for rock breakage by using an energy-based approach. The indentation stress intensity factor Kind and indentation cracking equation for rock-cutting/breakage have thus been formulated analytically.

Composition dependence of indentation deformation and indentation cracking in glass

Crack initiation and deformation behaviors of oxide glasses belonging to different chemical systems were studied using the Vickers indentation test. The crack initiation resistance is chiefly governed by the extents to which densification and isochoric shear flow develop in a process zone beneath and within the contact area. Densification is favored in glasses with relatively small Poisson’s ratio (ν), whereas shear is favored at large ν. Glasses were ranged according to their resistance to the formation of corner cracks as follows: Resilient, for 0.15⩽ν⩽0.20; Semi-Resilient, for 0.20⩽ν⩽0.25; and Easily-Damaged for 0.25<ν<0.30. Radial-median cracks occur at low load (⩽50mN) in Easily-Damaged glasses, while cone cracks predominate in Resilient glasses under higher loads. A critical value for ν (∼0.22 depending on the Young’s modulus/hardness ratio) was identified, at which the intensity of the indentation stress field tends to vanish, preventing crack formation on loading, while the driving force on unloading remains very small.

Cohesive interface simulations of indentation cracking as a fracture toughness measurement method for brittle materials

Cracks in brittle solids induced by pyramidal indenters are ideal for toughness evaluation since the indentation stress fields decay rapidly from the contact center and any cracks will be eventually arrested. Thus, if the applied energy release rate can be determined analytically, the material toughness can be deduced by measuring the crack length. However, such a driving force calculation is a nontrivial task because of the complex stress fields; only a number of limit cases can be solved, such as the long half-penny cracks (at least two times larger than the contact size) in the classic Lawn–Evans–Marshall (LEM) model. Important questions such as the evolution from short cracks to median/radial and then to half-penny cracks, the form of the scaling relationship that relates fracture toughness to material hardness and indenter angles, the threshold load for indentation cracking, etc., cannot easily be answered without a detailed knowledge of the co-evolution history of the stress fields and crack morphology. To this end, a finite element model of four-sided pyramidal indentation adopting cohesive interface elements is developed to study the effects of indenter geometry, load, cohesive interface parameters, and material properties on the initiation and propagation of the median/radial/half-penny crack systems. The validity and artifacts of the cohesive interface model are carefully examined, and the crack morphologies under various indentation and material parameters are systematically studied. Numerical predictions lead to a quantitative evaluation of the threshold load for indentation fracture, and an improved method for the evaluation of material toughness from the indentation load, crack size, hardness, elastic constants, and indenter geometry, which compare favorably to a large set of experiments in the literature. It is also found that the toughness evaluation method is very sensitive to Poisson’s ratio – an observation that has previously received little attentions. An approximate analysis for short cracks is developed based on the fracture mechanics of annular cracks and the embedded-center-of-dilatation model for indentation-induced residual stress fields.

Plastic Domain Microstructure and Hardness Analysis of Indented Layered Composite

The size dependent hardening in Al-4wt%Cu thin film on Si substrate has been investigated by the numerical calculation of indentation stress field and the observation of plastic zone microstructure of indented film. Distribution of internal stress predicted by triangular dislocation loop (TDL) model shows no size dependency with the different number of dislocations when the constant line density is assumed at the contact surface. TEM cross-sectional observation reveals that the plastic deformation is dominantly induced inside the film, and the growth of plastic zone is restricted at the interface of hard Si substrate. The size dependent hardening in soft film and hard substrate system is discussed from the change in dislocation density with respect to the plastic zone microstructure.

Evaluation of critical strain for crack nucleation of magnesium di-boride superconductor using indentation method

To fulfill the promises of MgB 2 and MgB 2− x C x in superconducting electrical transportation, the components made by these materials need to undergo plastic work process, for which the knowledge of their mechanical behavior (i.e. elastoplastic and strength properties) is critical. This study proposes the use of a convenient method based on indentation to evaluate both the elastoplastic and strength properties of MgB 2 and MgB 2− x C x . Through the reverse analysis using dual sharp indenters, we first extract the yield stress and work hardening exponent quantitatively. Next, the critical stress for crack nucleation (fracture strength) is estimated from a combination of experiment and numerical simulation of indentation stress field using the deduced elastoplastic properties. The critical fracture strain of MgB 2 is evaluated to be reasonably close to that from conventional tensile test. We further show that in MgB 2− x C x , the material stiffness, yield stress and fracture strength are degraded due to carbon additive, while the work hardening exponent is slightly higher. Therefore, the addition of C does not improve the mechanical properties of MgB 2. The findings shed some useful light on the workability of MgB 2, and may become a basis for understanding the feasibility of fabrication and usage of superconductor (where the mechanical and electrical properties are coupled).

Brittle‐to‐ductile transition temperature in InP

AbstractDeformation experiments were conducted on monocrystalline InP by 4‐point bend tests as well as by conventional and depth‐sensing indentation (DSI) tests. Temperature ranges where the material exhibited a brittle or a ductile behavior were investigated with particular focus on the transition from one deformation mode to the other. The 4‐point bend tests show that InP exhibits a sharp brittle‐to‐ductile transition (BDT) temperature within 5° between 350 and 355 °C at a strain rate of 2.9 × 10−5 s−1. The indentation BDT (IBDT) temperature is found to be significantly lower at ∼250 °C. The difference of nearly 100 °C between the two techniques is attributed to the hydrostatic component of the indentation stress field that suppresses fracture and shifts the transition to a lower temperature.

Evaluation of biological cell properties using dynamic indentation measurement

Viscoelastic mechanical properties of biological cells are commonly measured using atomic force microscope (AFM) dynamic indentation with spherical tips. A semiempirical analysis based on numerical simulation is built to determine the cell mechanical properties. It is shown that the existing analysis cannot reflect the accurate values of cell elastic/dynamic modulus due to the effects of substrate, indenter tip size, and cell size. Among these factors, substrate not only increases the true contact radius but also interferes the indentation stress field, which can cause the overestimation of cell moduli. Typically, the substrate effect is much stronger than the other two influences in cell indentation; and, thus, the cell modulii are usually overestimated. It is estimated that the moduli can be overestimated by as high as over 200% using the existing analysis. In order to obtain the accurate properties of cells, correction factors that account for these effects are required in the existing analysis.

Nanomechanics of Coatings for Electronic and Optical Applications

In most coating applications damage resistance is controlled by the mechanical properties of the coating, interface and substrate. For electronic and optical applications the design of coating-substrate systems has been predominantly controlled by their functional properties but more recently the mechanical response of the system has been used to enhance functional properties, as in the case of strained silicon/SiGe microelectronic devices where tensile strain has been used to enhance mobility and increase device speed. As coatings become more complex, with multilayer and graded architectures now in widespread use, it is very important to obtain the mechanical properties (such as hardness, elastic modulus, fracture toughness, etc.) of individual coating layers for use in design calculations and have failure-related design criteria which are valid for such multilayer systems. Nanoindentation testing is often the only viable approach to assess the damage mechanisms and properties of very thin coatings (&lt;m) since it can operate at the required scale and provides fingerprint of the indentation response of the coating/substrate system. If coating properties are to be assessed, the key point is to ensure any measured value is free from the influence of the deforma-tion of the substrate or lower coating layers. Finite element analysis of indentation load displace-ment curves can be used to extract materials properties for design; as coating thicknesses decrease it is observed that the yield strength required to fit the curves increases and scale-dependent materials properties are essential for design. Since plasticity is less likely, non-linear elasticity is increasingly important as the size of a nanostructure is reduced. Similarly the assessment of fracture response of very thin coatings requires modeling of the indentation stress field and how it is modified by plas-ticity during the indentation cycle. An FE approach using a cohesive zone model has been used to assess the locus of failure and demonstrates the complexity of adhesive failure around indentations for multilayer coatings. Finally the mechanical design of a metallization stress sensor based on na-noindentation-derived materials properties, non-linear elastic and plastic behavior and the treatment of geometrical non-linearities (stress stiffening) is discussed.