Modelling and simulation of the hardness profile and its effect on the stress-strain behaviour of punched electrical steel sheets

The shear cutting of electrical steel sheets has a significant influence on the magnetic and mechanical material properties. Due to plastic deformation and strain hardening in the area of the punched edge, the electrical steel sheets exhibit a characteristic hardness profile. This study deals with the modelling of the resulting hardness profile by means of finite-element simulations. Elastic-plastic material properties are obtained from spherical nanoindentation testing as a function of the local hardness. In particular, representative stress-strain values are determined by applying Tabor's concept of indentation stress-strain curves. The choice of the appropriate stress- and strain-constraint factors is discussed with respect to the nanoindentation test setup used. Following this, the representative stress-strain values are analytically described to determine true stress-strain curves for the local assignment of different material models depending on the hardness. The implementation of the modelling approach in a finite-element simulation is presented for a punched electrical steel sheet specimen under monotonic loading. The simulation results are basically in good agreement with experimental data and confirm the expected influence on the mechanical material behaviour due to the shear cutting process.     

Determination of plastic yield stress from spherical indentation slope curve

The indentation slope curve from a spherical indentation on elastic-plastic materials is examined. By comparing it with that of an linear elastic material of the same elastic properties, we found that the start point of plastic yielding for an elastic-plastic material can be easily located from the indentation slope curve. Based on this analysis, a simple but effective method is proposed to measure the plastic yield stress of very small samples from a spherical nano-indentation slope curve.     

Indentation plasticity and microfracture in silicon carbide

The extent of the plastically deformed region associated with indentation in silicon carbide is determined by means of selected-area electron channelling. It is found that the extent of the plastic zone beneath an indent is quite large, i.e. equal to about five times the impression radius. Microcrack formation is studied in the SEM, and the combined results are discussed in terms of current elastic-plastic indentation fracture models. The first cracks to form are radial microcracks; their morphology, and the observed indentation plastic zone dimensions, support the elastic-plastic model of Perrott for indentation cracking in-SiC.     

Deformation Processes of Advanced Alloy in Indentation and Turning

A comparison of a dynamic indentation method with a quasi-static one is used to study evolution of penetration and a generated force in the indentation process. Turning (a machining process) and dynamic indentation techniques are expected to have similar ranges of strain, strain rate and stress values in the process zone of a workpiece in a case of similar kinematics and boundary conditions. Here, we study the underlying mechanics of these two techniques. Based on advanced finite-element models, similarities and differences between the indentation and turning processes are elucidated.This study demonstrates that some critical cutting parameters can be predicted from indentation process; however, noticeable differences in the underlying deformations do exist.     

Creep analysis of surface-cracked plates by a creep line-spring method

The creep line-spring method proposed in this paper is based on the solutions for the following two problems: a creep crack under non-steady creep condition; an elastic-plastic surface-cracked plate. For the problem of a non-steady creep crack, an engineering approach for estimating the load-line displacement, crack-tip J and C integrals is presented by extending the engineering approach for elastic-plastic fracture analysis to creep analysis. For solving the elastic-plastic surface crack, a simplified elastic-plastic line-spring method is applied. These two approximate solutions are checked by the finite element method. On the basis of the above two approximate methods, a creep line-spring method is proposed and the corresponding fundamental equations are established. The creep line-spring method is used to estimate creep fracture parameters for three-dimensional cracks. In order to check its accuracy, several surface-cracked plates under uniform tension are analyzed by the creep line-spring method and by the three-dimensional finite-element method. The numerical results show that the creep line-spring method is in good agreement with the finite-element method and has the same accuracy as the common elastic-plastic line-spring method.     

Elastic–plastic behaviour in materials loaded with a spherical indenter

Certain ceramic materials display an indentation response similar to that observed for ductile metals when loaded with a spherical indenter. This unusual behaviour, for what are nominally brittle materials, influences the mode of contact damage in applications such as machining, wear, impact damage and hardness testing. The shape of the plastic zone beneath the indenter is typically fully contained within the circle of contact on the specimen surface and thus conventional hardness theories, such as the popular expanding cavity model, provide an inadequate account of indentation response of the material. The present work demonstrates, by experiment, finite element modelling and theoretical considerations, that the indentation response is determined by the interaction between the evolving plastic zone and the mechanical properties of the specimen material, in particular, the ratio of the elastic modulus to the yield stress. This revised version was published online in November 2006 with corrections to the Cover Date.     

Scaling functions in conical indentation of elastic-plastic solids

Summary The finite element method was used to simulate the conical indentation of elastic-plastic solids with work hardening. The ratio of the initial yield strength to the Young’s modulus Y/E ranged from 0 to 0.02. Based on the calculation results, two sets of scaling functions for non-dimensional hardness H/K and indenter penetration h are presented in the paper, which have closed simple mathematical form and can be used easily for engineering application. Using the present scaling functions, indentation hardness and indentation loading curves can be easily obtained for a given set of material properties. Meanwhile one can use these scaling functions to obtain material parameters by an instrumented indentation load-displacement curve for loading and unloading if Young’s modulus E and Poisson’s ratio ν are known.     

A dual conical indentation technique based on FEA solutions for property evaluation

The sharp indenters such as Berkovich and conical indenters have a geometrical self-similarity so that we can obtain only one parameter from an indentation loading curve, which makes different materials have the same load-displacement relation. Most studies to evaluate elastic-plastic properties by using the geometrical self-similar indenter have therefore tried to use dual/plural indentation techniques, on the basis of the concept of representative strain/stress varying with the indenter angle. However, any suggested representative concept is not universally operative for real materials. In this work, we suggest a method of material property evaluation without using the concept of representative strain. We begin the work by studying the characteristics of load-depth curves of conical indenters via finite element (FE) method. From FE analyses of dual-conical indentation, we investigate the relationships between indentation parameters and load-depth curves. The projected contact diameter is expressed as a function of the indenter angle, tip-radius, and material properties, which allows us to simply predict the elastic modulus. Two mapping functions for two indenter angles (45° and 70.3°) are presented to find the two unknowns (yield strain and strain-hardening exponent) via dual indentation technique. The method provides elastic modulus, yield strength and strain-hardening exponent with an average error of less than 5%. The method is valid for any elastically deforming indenters. We also discuss the sensitivity of measured properties to the load-displacement curve variation, and the difference between conical and Berkovich indenters.     

Threshold microfracture during elastic-plastic indentation of ceramics

It is shown that for a variety of ceramics the threshold for microfracture during elastic-plastic indentation corresponds to radial, rather than subsurface median, crack formation. This is contrary to the fundamental assumption of current models for threshold crack nucleation by sharp indenters. The significance of this observation in terms of strength reduction is discussed.     

Analysis on elastic-plastic spherical contact and its deformation regimes, the one parameter regime and two parameter regime, by finite element simulation

In this paper the contact problem of a rigid sphere against an elastic-plastic sphere and a spherical elastic-plastic cavity is studied by means of finite element simulation for a wide range of radius ratios. Our results indicate that the deformation range naturally divides into two regimes, i.e. a one parameter regime (covering the elastic, small elastic-plastic and similarity deformation) and a two parameter regime (covering the finite deformation). In these two regimes average contact pressures (as well as contact area) versus indentation depth can be described respectively by the single parameter, i.e. indentation depth h/R_e, and the two parameters, i.e. h/R_e and radius ratio R₁/R₂. Moreover, the variation trends of average contact pressure with the increase of indentation depth differ markedly in different deformation regimes. The numerical evolution of pressure distribution indicates that with increase of indentation depth the pressure distribution becomes more peaked at the center of the contact area meanwhile the maximum contact pressure, limited by the flow stress, increases slightly. Therefore in the two parameter regime, the average pressure would stop growing and get lower rather than continuously higher as it does in the one parameter regime.     

平头压痕试验确定薄膜弹塑性参数的研究

本文研究用平头压痕试验确定薄膜-基体材料中薄膜材料弹塑性参数的可行性,重点研究了薄膜材料的屈服强度和硬化模量的确定方法.利用有限元(FEM)进行了模拟计算,给出了平头压痕下典型的等应力分布,以及载荷-压入深度的曲线.通过对载荷-压入深度曲线的研究,给出了通过平头压痕试验确定薄膜屈服强度和薄膜硬化模量的方法.     

Twyman effect mechanics in grinding and microgrinding

In the Twyman effect (1905), when one side of a thin plate with both sides polished is ground, the plate bends: The ground side becomes convex and is in a state of compressive residual stress, described in terms of force per unit length (Newtons per meter) induced by grinding, the stress (Newtons per square meter) induced by grinding, and the depth of the compressive layer (micrometers). We describe and correlate experiments on optical glasses from the literature in conditions of loose abrasive grinding (lapping at fixed nominal pressure, with abrasives 4-400 μm in size) and deterministic microgrinding experiments (at a fixed infeed rate) conducted at the Center for Optics Manufacturing with bound diamond abrasive tools (with a diamond size of 3-40 μm, embedded in metallic bond) and loose abrasive microgrinding (abrasives of less than 3 μm in size). In brittle grinding conditions, the grinding force and the depth of the compressive layer correlate well with glass mechanical properties describing the fracture process, such as indentation crack size. The maximum surface residual compressive stress decreases, and the depth of the compressive layer increases with increasing abrasive size. In lapping conditions the depth of the abrasive grain penetration into the glass surface scales with the surface roughness, and both are determined primarily by glass hardness and secondarily by Young's modulus for various abrasive sizes and coolants. In the limit of small abrasive size (ductile-mode grinding), the maximum surface compressive stress achieved is near the yield stress of the glass, in agreement with finite-element simulations of indentation in elastic-plastic solids.     

Examination of local variations in viscous,elastic, and plastic indentation responses in healing bone

A viscous-elastic-plastic indentation model was used to assess the local variability of properties in healing porcine bone. Constant loading- and unloading-rate depth-sensing indentation tests were performed and properties were computed from nonlinear curve-fits of the unloading displacement-time data. Three properties were obtained from the fit: modulus (the coefficient of an elastic reversible process), hardness (the coefficient of a nonreversible, time-independent process) and viscosity (the coefficient of a nonreversible, time-dependent process). The region adjacent to the dental implant interface demonstrated a slightly depressed elastic modulus along with an increase in local time-dependence (smaller viscosity); there was no clear trend in bone hardness with respect to the implant interface. Values of the elastic modulus and calculated contact hardness were comparable to those obtained in studies utilizing traditional elastic-plastic analysis techniques. The current approach to indentation data analysis shows promise for materials with time-dependent indentation responses.     

Strain and stress fields near the blunted tip of a crack under mixed mode loading and the implications for fracture

The strain distribution in the vacinity of a blunted crack-tip is analysed by slip line theory under the conditions of plane-strain, small-scale yielding, and mixed-mode loading of Modes I and II. A generalized crack-tip opening displacement is introduced by which the strain and stress fields near the blunted crack-tip are determined uniquely over a wide range of Mode I and II combinations. Also, coupled experimental and finite-element analyses under the condition of large-scale yielding reveal that the initiation of stable crack growth occurs when the generalized crack-tip opening displacement attains a critical value which is constant for the material tested. The finite-element analysis is based on the finite deformation theory of elastic-plastic materials. The generalized crack-tip opening displacement criterion is found to be superior to the J-integral and the usual COD for the characterization of the initiation of stable crack growth. The plastic work in a small circular region at the crack-tip is found to be equivalent to the generalized crack-tip opening displacement, as a fracture criterion.     

Two-step method to evaluate equibiaxial residual stress of metal surface based on micro-indentation tests

The present study proposed a method to evaluate the equibiaxial compressive residual stress of a metal surface by means of a depth-sensing indentation method using a spherical indenter. Inverse analysis using the elastic–plastic finite-element model for an indentation test was established to evaluate residual stress from the indentation load–depth curve. The proposed inverse analysis utilizes two indentation test results for a reference specimen whose residual stress is already known and for a target specimen whose residual stress is unknown, in order to exclude the effect of other unknown mechanical properties, such as Young’s modulus and yield stress. Residual stress estimated by using the indentation method is almost identical to that measured by X-ray diffraction for indentation loads of 0.49–0.98 N. Therefore, it can be concluded that the proposed method can effectively evaluate residual stress on metal surface.     

An Inverse Approach for Extracting Elastic-plastic Properties of Thin Films from Small Scale Sharp Indentation

An inverse method for extracting the elastic-plastic properties of metallic thin films from instrumented sharp indentation has been proposed in terms of dimensional analysis and finite element modeling.A wide range of materials with different elastic modulus,yield strength,and strain-hardening exponent were examined.Similar to the Nix-Gao model for the depth dependence of hardness H,(H/H0)2=1+h*Hh,the relationship between elastic modulus E and indentation depth h can be expressed as(E/E0)4=1+h*Eh.By combining these two formulas,we find that there is a relationship between yield stress σ y and indentation depth h:σy = σy0·(1+h*Hh)f(n)·(1+h*Eh)[0.25-0.54f(n)],where σ y0 is the yield strength associated with the strainhardening exponent n,the true hardness H0 and the true elastic modulus E0.f(n)= 1/2(1-n) is constant,which is only related to n,and h*H and h*E are characteristic lengths for hardness and elastic modulus.The results obtained from inverse analysis show that the elastic-plastic properties of thin films can be uniquely extracted from the solution of this relationship when the indentation size effect has to be taken into account.     

获取材料本构关系和硬度的压入法研究

依据锥形压入试验和弹塑性接触有限元分析,提出基于能量原理预测金属材料本构关系的CR-EMI方法。通过该方法揭示锥形压入能量比与表征应力之间存在线性律,提出通过压入曲线(P-h曲线)获取材料本构关系的关系式,根据Hollomon本构关系模型预测硬度的H-EMI方法。通过对多种金属材料进行压入试验和有限元分析,验证CR-EMI方法和H-EMI方法的有效性与精确性。     

Power losses in bent and elongated polymer optical fibers

This study performs experimental and numerical investigations into the power losses induced in bent, elongated polymer optical fibers (POFs). The theoretical analysis is based on a three-dimensional elastic-plastic finite-element model and makes the assumption of a planar waveguide. The finite-element model is used to calculate the deformation of the elongated POFs such that the power loss can be analytically derived. The effect of bending on the power loss is examined by considering seven different bend radii ranging from 10 to 50 mm. The results show that bending and elongation have a significant effect on the power loss in POFs. The contribution of skew rays to the overall power loss in bent, elongated POFs is not obvious at large radii of curvature but becomes more significant as the radius is reduced.     

Effect of elongation deformation on power losses in polymer optical fibers

We investigate the effect of fiber elongation on power loss as rays propagate along deformed polymer optical fibers (POFs). Variations in core diameter, incident angle, stress and strain distributions, and necking of the POFs during fiber elongation are studied. The power losses in the deformed POFs are analyzed both experimentally and numerically. Theoretical analysis based on an elastic-plastic finite-element model and a planar waveguide assumption is proposed. It is found that fiber elongation significantly affects the power loss in POFs, particularly at higher values of elongation. Good agreement between the measured results and the results simulated from the proposed model is obtained. The maximum difference is less than 5%. Results indicate that the proposed theoretical analysis based on an elastic-plastic finite-element model and a planar waveguide assumption is feasible to predict the power loss variation introduced by elongated deformations. A curve-fitted equation is also proposed to estimate the power loss of POFs under different fiber elongation conditions.     

Effect of soft substrate on the indentation damage in silicon carbide deposited on graphite

Indentation-induced damage is investigated in silicon carbide (SiC) deposited on graphite substrate. The SiC films have been grown by LPCVD (Low Pressure Chemical Vapor Deposition) method using MTS (CH₃SiCl₃) as a source gas and H₂ as a diluent gas to provide highly dense deposited layer and strong interfacial bonding. The elastic-plastic mismatch is very high to induce distinctive damages in the coating and the substrate layer. The specimens with various coating thicknesses are prepared by changing CVD condition or mechanical polishing. Indentation damages with different sizes are introduced by controlling indentation load in Nanoindentation, Vickers indentation and Hertzian indentation test. Basic mechanical properties such as hardness, toughness, elastic modulus are evaluated against coating thickness. Mechanical properties are sensitive to the indentation load and coating thickness. The results indicate that coating thickness has a vital importance on the design of hard coating/soft substrate system because the soft substrate affects on the mechanical properties.