Dundurs Parameters Research Articles

Analysis of tangential stress response of ice-workpiece interface in ice-based machining of thin-walled parts: Modeling and experiment

The contact stress between the fixture and the workpiece surface is a crucial factor in evaluating the constraint performance of the fixture. According to the concept of an ice-based fixturing(IBF) proposed by the author, this paper conducts a modeling and experimental study of the tangential stress response at the ice-workpiece interface during ice-based machining. Initially, the principle of IBF is explained. Subsequently, the Dundurs parameters are used to characterize the mechanical properties of the ice-workpiece interface. According to the interface continuous conditions of stress and displacement, a predictive model for the tangential stress at the ice-workpiece interface is established using the Goursat formula. Afterwards, interface temperature experiments are carried out to analyze the temperature state of the ice-workpiece interface. Finally, milling experiments are conducted to analyze the variation of cutting force and interface tangential stress with the thickness of TWP, and to verify the accuracy of the analytical model. This study can provide valuable references for the evaluation of the constraint state of the fixture.

Prediction of icing interface normal stress response for thin-walled parts machining with ice-based fixturing (IBF)

Fixtures can maintain stability in the machining of thin-walled parts (TWP), thus avoiding the occurrence of workpiece deformation. The stress at the fixture-workpiece contact interface is a key factor in evaluating the reliability of the fixture’s restraint on the TWP. This paper investigates the prediction of icing interface normal stress during TWP milling based on the ice-based fixturing (IBF) previously proposed by the authors of this paper. The principle of the IBF is first explained. The mechanical properties of the ice-workpiece bonding material (IWBM) are then characterized by Dundurs parameters. Afterwards, an analytical model for the prediction of icing interface normal stress under cutting load is developed using the Goursat formula based on the interface continuity conditions of stress and displacement. The finite element method (FEM) is then used to verify the accuracy of the prediction model, and the results show that the average prediction error of the icing interface normal stress is limited to 13.99%. Finally, milling experiments are carried out to verify the validity of the finite element model, and the experimental results show that the simulation errors of the main cutting force and feeding force are limited to 12.35% and 11.47% respectively, and the FEM can greatly simulate the cutting state of the workpiece clamped by IBF. This paper can provide a valuable theoretical and practical basis for the analysis and prediction of stress at the workpiece-fixture contact interface.

Buckling-induced delamination: Connection between mode-mixity and Dundurs parameters

Modern electronics, micromechanical devices and applications demanding high reliability to weight or cost ratio consist of various combinations of multilayered thin films on rigid and compliant substrates, whereas the used materials can differ in their mechanical properties. In recent years, differences in the elastic moduli and Poisson’s ratios of such structures are becoming more pronounced. Therefore, a strong push to investigate interface stability with a more in-depth view on the elastic material properties mismatch influence is needed. Measurements of the adhesion of thin films on different substrate materials can be easily performed by the spontaneous buckling method described by Hutchinson and Suo. However, the original approach assumes several simplifications. One is to omit the changes of the influence of the elastic mismatch between the thin film and substrate on the basis of small variations in then-used materials, which is not true for modern materials combinations with vastly different elastic properties. The elastic mismatch on the interface between two different materials can be described by the Dundurs parameters. In this work, finite element modelling is combined with analytical solutions according to general description of the original model to extend the usability of the Hutchinson and Suo method for use with more different materials with higher accuracy. Obtained results point out the fact that disregarding the Dundurs parameters introduces significant errors in evaluating adhesion energy in relation to loading mode, proving the necessity to properly include elastic mismatch.

Extended JKR theory on adhesive contact of coated spheres

Thin films, coatings, and layered structures are ubiquitous in contemporary micro- and nanoelectronics, optoelectronics, and electromechanical systems, for which adhesion between heterogeneous materials is one of the important mechanical properties to be considered in fabrication and operation. In this study, the adhesive contact between elastic layered spheres, which includes a thin film on a flat substrate as a special case, is analyzed on the basis of the conventional Johnson–Kendall–Roberts (JKR) theory on adhesive contact between elastic spheres. Firstly, the force–depth relations of axisymmetric flat and spherical indentations on an elastic film perfectly bonded to an elastic half-space are obtained in compact forms, depending on two Dundurs parameters and the ratio of the contact radius to the thickness of the film. The solution of a spherical indentation on a layered half-space is then superposed, following a Hertz analysis, to obtain the adhesionless Hertzian contact between the elastic films coated on the elastic spheres. Similarly, the solution to the adhesive JKR contact state between elastic films coated on elastic spheres is also obtained by properly superposing the linear elastic solutions of the flat and spherical indentations on a layered half-space. The obtained Hertzian and adhesive JKR contact states should be regarded as approximate solutions, since the pressure distribution in the contact region does not exactly satisfy Newton’s third law. The JKR state equations among the normalized applied force, normalized penetration depth, and normalized contact radius are obtained in compact forms, in which non-dimensional multiplying factors depending on the geometric parameters and two sets of non-dimensional Dundurs parameters account for the effect of the elastic layers. Finally, the pull-off force at the moment of debonding of the two elastic films coated on the elastic spheres is calculated and compared with the conventional JKR result.

Critical value of the generalized stress intensity factor for a crack perpendicular to an interface

When a crack tip impinges upon a bi-material interface, the order of the stress singularity will be equal to, less than or greater than one-half. The generalized stress intensity factors have already been determined for some such configurations, including when a finite-length crack is perpendicular to the interface. However, for these non-square-root singular stresses, the determination of the conditions for crack growth are not well established. In this investigation, the critical value of the generalized stress intensity factor for tensile loading is related to the work of adhesion by using a cohesive zone model in an asymptotic analysis of the separation near the crack tip. It is found that the critical value of the generalized stress intensity factor depends upon the maximum stress of the cohesive zone model, as well as on the Dundurs parameters (αandβ). As expected this dependence on the cohesive stress vanishes as the material contrast is reduced, in which case the order of the singularity approaches one-half.

Two Analytical Models to Determine the Stress Singularities in Elastic-Viscoelastic Joints

The stress singularities are obtained by two methods in elastic-viscoelastic joints, one is extending the corresponding solutions for elastic-elastic joints by using elastic-viscoelastic correspondence principles and the other is replacing the elastic material parameters with viscoelastic ones in Dundurs parameters directly. The difference between the two methods and the validity are discussed.

Notched-Butt Test for the Determination of Adhesion Strength at Bimaterial Interfaces

For the experimental determination of adhesion strength between materials it is desirable to have a uniform stress distribution within the interface of the specimen. The common butt-test with a flat interface between two adhering materials produces stress singularities at the edges of the specimen but shows uniform stress distribution along the interface within the material. To avoid a premature failure at the edge due to the presence of the singular stress field, a notch can be machined at the interface within one of the materials. For isotropic materials, the notch geometry depends on the Dundurs parameters of the bimaterial system. This notch produces a certain local material angle and eliminates stress singularities at the specimen edges. Analytical and finite-element calculations provide the notch geometry appropriate for uniform stress distribution along the whole interface. The applicability of the test is proven by the determination of adhesion strength between polycarbonate and thermoplastic polyurethane.

Influence of the Resin Layer Thickness at the Interface of Hybrid Metal-composite Co-cured Joints

As discussed in literature, the accurate analysis of the modern co-cured joints between composite materials or between a metal and a composite material (hybrid joints) is complicated by the influence of the interface resin layer on the interface singular stress field. In such joints, in fact, there is not a proper adhesive layer and the thickness of the resin layer, that plays the role of the adhesive, is not constant due to the presence of the reinforcing fibers in the composite adherent. For this reason several authors assume that a generic co-cured joint can not be studied as a simple bi-material joint, without considering the particular characteristics of the actual resin layer. This problem is also involved into the development of reliable design methods able to give accurate predictions of the joint efficiency. In this work, by theoretical analyses performed by using the Lekhnitskii theory, numerical simulations carried out by means of the boundary element method and experimental investigations based on the combined use of the generalized Dundurs parameters and digital photoelasticity, the influence of the resin layer on the singular stress field at the interface of a generic hybrid metal-composite joint, has been investigated.

Effective elastic modulus of film-on-substrate systems under normal and tangential contact

Load and depth sensing indentation methods have been widely used to characterize the mechanical properties of the thin film–substrate systems. The measurement accuracy critically depends on our knowledge of the effective elastic modulus of this heterogeneous system. In this work, based on the exact solution of the Green's function in Fourier space, we have derived an analytical relationship between the surface tractions and displacements, which depends on the ratio of the film thickness to contact size and the generalized Dundurs parameters that describe the modulus mismatch between the film and substrate materials. The use of the cumulative superposition method shows that the contact stiffness of any axisymmetric contact is the same as that of a flat-ended punch contact. Therefore, assuming a surface traction of the form of [1−( r/ a) 2] −1/2 with radial coordinate r and contact size a, we can obtain an approximate representation of the effective elastic moduli, which agree extremely well with the finite element simulations for both normal and tangential contacts. Motivated by a recently developed multidimensional nanocontact system, we also explore the dependence of the ratio of tangential to normal contact stiffness on the ratio of film thickness to contact radius and the Dundurs parameters. The analytical representations of the correction factors in the relationship between the contact stiffness and effective modulus are derived at infinite friction conditions.

Analysis of vertical cracking phenomena in tensile-strained epitaxial film on a substrate: Part I. Mathematical formulation

This paper presents an analysis of a single vertical crack and periodically distributed vertical cracks in an epitaxial film on a semi-infinite substrate where the cracks penetrate into the substrate. The film and substrate materials have different anisotropic elastic constants, necessitating Stroh formalism in the analysis. The misfit strain due to the lattice mismatch between the film and the substrate serves as the driving force for crack formation. The solution for a dislocation in an anisotropic trimaterial is used as a Green function, so that the cracks are modeled as the continuous distributions of dislocations to yield the singular integral equations of Cauchy-type. The Gauss–Chebyshev quadrature formula is adopted to solve the singular integral equations numerically. Energy arguments provide the critical condition for crack formation, at which the cracks are energetically favorable configurations, in terms of the ratio of the penetration depth into the substrate to the film thickness, the ratio of the spacing of the periodic cracks to the film thickness, and the generalized Dundurs parameters between the film and substrate materials.

The Effect of Material Property Gradient on the Fracture Toughness of a PMMA/PC Bimaterial with a Crack Normal to the Interface

Fracture toughness tests on CT specimens were carried out to study the fracture behavior for a crack lying perpendicular to the interface in a PMMA/PC bimaterial. Polymethylmethacrylate Acrylic (PMMA) and Polycarbonate (PC) cylindrical rods were joined together using the friction welding process. CT specimens were machined out of the bimaterial cylindrical rods. A sharp crack was introduced into the specimen perpendicular to and terminating at the bimaterial interface. Specimens including monolithic and bimaterial were loaded to fracture and experimental values of K were obtained. Finite element analysis was used to find out the stresses IC in the specimens. Subsequently the stress values were used to find out the fracture toughness of eac h specimen. It was found that the K values for bimaterial specimen could not be achieved by utilizing the inverse IC square root singularity in stress but it was dependent upon Dundurs parameters for bimaterials.

Influence of interface on fatigue threshold values in elastic bimaterials

This paper describes a study of the behavior of a fatigue crack growing in one elastic material and penetrating through the interface into a second material. The study aims especially to quantify the influence of the elastic mismatch of both materials on the threshold value of a fatigue crack propagating perpendicularly to the interface. Special attention is devoted to the case of a crack touching the interface. It is shown that the corresponding threshold value is strongly influenced by the existence of an interface between the two materials. A tentative procedure suggested in the paper makes it possible to quantify the effect and determine the dependence of the threshold value of a fatigue crack growing through the interface on the Dundurs parameters α and β. The results are applied to a body with a protective layer, and the corresponding fatigue threshold value for a crack with its tip at the interface is estimated. This makes it possible to decide whether the crack will stop at the interface or continue growing into the second material. The results generally contribute to a better understanding of the failure of bi-material bodies and of structures with protective layers.

Intensity factors for subinterface cracks in dissimilar anisotropic piezoelectric media

A subinterface crack paralleling an interface between two dissimilar piezoelectric solids is considered. When the distance between the interface and the crack is small compared to all other in-plane lengths, the problem can be analyzed as an asymptotic problem for a semi-infinite crack lying at some distance away from the interface. An integral equation for the asymptotic subinterface crack is derived, and a solution of the integral equation for small-generalized Dundurs parameters is obtained. Relations between the intensity factors for the subinterface crack and interface intensity factors of the corresponding interface crack are obtained for a conducting crack as well as for an insulating one.

Stress intensity formulas for three-dimensional cracks in homogeneous and bonded dissimilar materials

This paper is concerned with maximum stress intensity factors of arbitrary shaped defects or cracks under mixed mode loading and also cracks terminating at an interface. A convenient formula is proposed in terms of area parameter, where “area” is the projected area of the defects or cracks. First, a rectangular crack under mixed mode loading is considered with varying the aspect ratio and compared with the results of elliptical cracks. Then, area parameter is found to be useful under mixed mode loading. Second, a rectangular crack, which is perpendicular to and terminating at a bimaterial interface, is investigated with varying the combinations of materials constants. At the crack front the maximum stress intensity factors are expressed as a function of the elastic ratio of the materials. On the other hand, the generalized stress intensity factors at the interface are expressed as a function of Dundurs parameters α and β. Proposed formulas are usefully evaluating defects with any aspect ratio under any combinations of the materials.

On the Manipulation of Nanoscale Self-Assembly by Elastic Field

ABSTRACTMorphological and compositional self-assembly can be manipulated by the long-range elastic field. This paper gives a universal formulation that determines the dependence of energetically favored orientation of those self-assembled structures on the elastic interaction. Elasticity anisotropy can lead to symmetry breaking and herringbone structures. A layered substrate can tune the feature size by modulus mismatch, or tune the orientation if the layers have different orientation preference, or guide the self-assembly by embedded structures. A closed-form result is derived for elastically isotropic layers by using Dundurs parameters. The self-assembled structures can also be affected by a nonuniform residual stress field or external force field. Higher order (nonlinear) perturbation theory, coupling between morphology and composition, and other issues are also addressed in the discussion.

Stress singularity analyses of interface ends in micro-mechanics tests

Singular stress fields exist in the interface ends of micro-mechanics test specimens, which are used to measure the interfacial shear strength (IFSS) in fiber composites. With the aid of asymptotic and variable separation, the stress singularities near the axisymmetric interface ends are studied. The results show that the α-β diagram of the stress singularity exponents for the push-in specimen can be divided into two areas, singular and non-singular. The oscillatory singular area may appear in the diagram of a pull-out specimen. In the micro-droplet specimen, the oscillatory area is dependent not only on Dundurs parameters but also on the angle between the boundaries of the matrix and fiber. The general forms of angular distribution functions are derived in this paper. By the use of axisymmetric BEM and the obtained angular distribution functions, the numerical results of stress distribution near the interface end and the stress intensity factors are obtained. It is concluded that, theoretically, the interfacial shear strength (IFSS) cannot be determined by the existing interfacial micro-mechanics tests.

異種接合界面に接するき裂の√￣ａ￣ｒ￣ｅ￣ａパラメータによる応力拡大係数評価式

To evaluate arbitrary shaped defects or cracks terminating at an interface, a formula is proposed in terms of Murakami's √area parameter for the maximum stress intensity factors. Here “area” is the projected area of the defects or cracks. First, the solution for a rectangular crack, which is perpendicular to and terminating at a bimaterial interface, is considered with varying the aspect ratio of the crack and combinations of materials constants systematically. Then, the maximum stress intensity factors at the other side of the interface are expressed as a function of the elastic ratio of the materials. On the other hand, the general stress intensity factors at the interface is expressed as a function of Dundurs parameters α and β. Those expressions are usefully evaluating the defects under any combinations of the materials.

Mechanical analyses of the emplacement of laccoliths and lopoliths

Elastic deformations of host rocks during the emplacement within the Earth's crust of magmatic intrusions, such as laccoliths and lopoliths, are analyzed. The present analysis is built upon semianalytic elastic solutions for a pressurized horizontal crack buried between an overburden and a semi‐infinite base. The current work improves upon recent analyses by including several important features inherent to the development of laccoliths and lopoliths. First, both elongated intrusions (plane strain case) and circular intrusions (axisymmetric case) are described by the current models. Second, the effect of the difference in elastic moduli between the overburden and the substrate is considered. This difference in elastic moduli is characterized by one of the Dundurs parameters. Third, the stress intensity factor at the tip of the crack is assumed to be zero. Thus the stresses are finite, and the obtained laccolithic shapes are doubly hinged with horizontal slopes at the peripheries, as observed in the field. Fourth, unlike plate bending models, which are commonly used for major laccoliths, the current models describe a full range of ratios of intrusion width to overburden thickness. Numerical results are obtained for different combinations of the geometrical parameters, the material contrast and the driving pressure distributions. Graphs of these results confirm the plate bending model for large laccoliths, support Gilbert's concept pertaining to small laccoliths, permit the prediction of the sill‐laccolith transition, allow the analysis of the asymmetry in the vertical displacements above and below the intrusion, and lead to a possible mechanism of deep lopoliths emplacements. Some of the obtained results are compared to the available field data from the Henry Mountains.

TRANSIENT THERMOELASTIC ANALYSIS FOR TWO-DIMENSIONAL DISSIMILAR MATERIALS BY THE BOUNDARY ELEMENT METHOD

This article deals with the transient thermoelastic analysis for dissimilar materials under the plane strain condition. In the process of the boundary element formulation, the time-dependent fundamental solution for the transient heat conduction problem and the thermoelastic displacement potential for the transient thermal stress problem are introduced. Consequently, domain integrals are completely eliminated. The discretization based on the domain combination method for these boundary integral equations is implemented, and the transient temperature and stress fields are analyzed numerically. The transient temperature at the lateral surface and the transient thermal stress at the interface are investigated for the three categories that have been determined according to the characteristic equation expressed by Dundurs parameters.

Dependence of Stress Singular Fields on Material Combination of Butt-Jointed Plates Subjected Uniform Tension.

The near-tip stress fields around an interface edge of butt-jointed plates subjected uniform tension are analyzed by finite element method. Based on the result the dependence of the singular stress fields around the interface edge on the material combination is discussed. The relation between the exponent of the stress singularity and its intensity is investigated. The uniqueness of the intensity of singular stress fields for Dundurs's parameters is also studied. The equations which is useful for materials selection of joint concerning with the stress singularity are newly developed.