Increase of stress intensity near interface edge of elastic-creep Bi-material under a sustained load

The transition from small-scale creep to large-scale creep ahead of a crack tip or an interface edge with strong elastic stress singularity at the loading instant causes stress relaxation and the decrease of stress intensity in general. However, this study shows that the stress near the interface edge of bi-material with no or weak elastic stress singularity increases after the loading instant and brings about the stress concentration during the transition. In addition, the creep strain distribution of this bi-material after the loading instant is different from that occurred in the transition of an interface edge with strong elastic stress singularity or a crack tip (notch root). The criterion for the increase or decrease of stress intensity near the interface edge proved by the finite element method is proposed in this study. The stress intensity near the interface edge increases when the elastic stress singularity is lower than the creep stress singularity (λ^el < λ^cr) and vice versa.     

Stress field near interface edge of elastic-creep bi-material

Stress fields on elastic-creep bi-material interfaces with different geometry of the interface edge are analyzed by finite element method. The results reveal that the stress highly concentrates near the interface edge at the loading instant and it gradually decreases as the creep-dominated zone expands from the small-scale creep to the large-scale creep. The stress singularity due to creep which resembles the HRR stress singularity appears near the interface edge in all cases. The stress intensity near the interface edge time-dependently decreases and becomes constant when the transition reaches the steady state. The magnitude is scarcely influenced by the edge shape of elastic material, though it depends on the edge shape of creep material. The stress intensity during the transition can be approximately predicted by the J-integral at the loading instant.     

An interface crack between an orthotropic thin film and substrate

This work is concerned with a semi-infinite interface crack between a thin film and a substrate. The two materials are assumed to be linearly elastic and orthotropic. A solution is presented for the stress field due to an edge dislocation on the interface which is valid for any combinations of material parameters. It is found that the behavior of such a bi-material system is governed by 6 independent material parameters. The stress intensity factor is computed for general edge loadings by solving integral equations numerically, and the size of the K-dominant zone is also studied for a residually stressed thin film. The situations in which the K-field zone of dominance is very small are identified and discussed.     

A generalized screw dislocation near a wedge-shaped magnetoelectroelastic bi-material interface

The magnetoelectroelastic solution of a generalized screw dislocation interacting with a wedge-shaped magnetoelectroelastic bi-material interface is derived in this paper. The screw dislocation is assumed to be straight and infinitely long in the z-direction and suffers a finite discontinuity in the displacement, electric potential and magnetic potential across the slip plane. The explicit closed-form analytical solution for the generalized stress field is derived by means of the complex variable and conformal mapping methods. The generalized stress intensity factors of the wedge tip induced by the dislocation and the image force acting on the dislocation are formulated and calculated. The influence of the wedge angle and the different bi-material constant combinations on the image force is discussed. Numerical examples for three particular wedge angles are calculated and compared with other available results.     

Complex variable method of computing Jk for bi-material interface cracks

A method using functions of a complex variable is developed for evaluation of J₁ and a modified J₂ integrals for bi-material interface cracks. This method, used in conjunction with the finite element method, would be useful in the prediction of stress intensity factors for cracks lying between the interface of two dissimilar materials. Since the direct evaluation of J₂ poses difficulties in modeling the singular behavior in the near vicinity around the crack tip for bi-material crack problems, it is modified by evaluating it around a contour path of small radius from the crack tip within the singularity dominated zone. It is shown that the stress intensity factors for a bi-material interface crack can be accurately evaluated using these j_k integrals.     

Initiation of interface crack at free edge between thin films with weak stress singularity

Delamination tests using sandwich type specimens are conducted for eight combinations of materials: thin films formed on silicon substrates which are relatively popular in micro-electronic industry, to develop a method for quantitative evaluation and comparison of crack initiation strength at the free edge. The difficulty stems from the difference of stress singularity, K_ij/r^λ (K_ij: stress intensity, r: distance from free edge and λ: order of stress singularity), where λ is depending on the combination of materials. Thus, the critical K_ij has different dimensions, MPa m^λ, in each interface. Using the experimentally observed delamination load, the stress distribution along the interface is analyzed by boundary element method. Since the orders of stress singularity, λ, in the materials are less than 0.07 (weak singularity), the stress field near the interface edge is almost constant in atomic (nanometer) level. Then, the critical strength for the interface cracking is quantitatively represented by the concentrated stress near the edge. The effects of the several factors such as species of thin films, oxidized interlayers and deposition processes of thin films on the interface strength are evaluated on the basis of this critical stress as well.     

Edge dislocations near a cracked sliding interface

The edge dislocations near a cracked sliding interface were investigated. A continuous distribution of edge dislocations with Burgers vector along the y direction was used to simulate a crack of finite length along the sliding interface. From the dislocation distribution the stress field in the entire space was obtained. The stress intensity factors at both crack tips and image force on the edge dislocation were derived. The effects of the dislocation source and shear modulus ratio on both stress intensity factors and image force were also studied. Only mode I stress intensity factors at both tips were found in the composite materials with a sliding interface. The edge dislocations with Burgers vector along the y direction emitted from the crack always shield it to prevent propagation. The above results may reduce to an edge dislocation near a semi-infinite crack along a sliding interface including a sliding grain boundary. This revised version was published online in August 2006 with corrections to the Cover Date.     

Disappearance of stress singularity at interface edge due to nanostructured thin film

The purpose of this study is to examine the stress distribution near the interface between a nanostructured thin film and a solid body. We focus on a nanostructured thin film that consists of Ta₂O₅ helical nanosprings fabricated on a Si substrate by dynamic oblique deposition. The mechanical properties of the thin film are obtained by vertical and lateral loading tests using a diamond tip built into an atomic force microscope. The apparent shear and Young’s moduli, G′ and E′, of the thin film are 2-3 orders of magnitude lower than those of a conventional solid Ta₂O₅ film. Moreover, the thin film shows strong anisotropy. A finite element analysis for two types of components with different interface edges between the thin film and an elastic solid body is conducted under uniform displacement. One has a free edge where the surface-interface angle is 90°-90°, and the other has a short interface crack. These analyses indicate the absence of not only stress singularity but also high stress concentration near the free edge and the interface crack tip. The characteristic stress distributions near the interface are due to the nanoscopically discrete structure of the thin film.     

The effect of material combinations and relative crack size to the stress intensity factors at the crack tip of a bi-material bonded strip

Several types of singular stress fields may appear at the corner where an interface between two bonded materials intersects a traction-free edge depending on the material combinations. Since the failure of the multi-layer systems often originates at the free-edge corner, the analysis of the edge interface crack is the most fundamental to simulate crack extension. In this study, the stress intensity factors for an edge interfacial crack in a bi-material bonded strip subjected to longitudinal tensile stress are evaluated for various combinations of materials using the finite element method. Then, the stress intensity factors are calculated systematically with varying the relative crack sizes from shallow to very deep cracks. Finally, the variations of stress intensity factors of a bi-material bonded strip are discussed with varying the relative crack size and material combinations. This investigation may contribute to a better understanding of the initiation and propagation of the interfacial cracks.     

Interaction of an edge dislocation with a lamellar inhomogeneity

The elastic behavior of an edge dislocation parallel to an infinite lamellar inhomogeneity is considered. The elastic field in the matrix and lamella is obtained through the complex variable technique and the image method. The resulting formulas may be employed to solve the elasticity problem for any source of internal stress (plane elasticity) whose bulk field is known. The force on the dislocation is explicitly calculated and discussed. It is found that the behavior of the dislocation near a lamella differs in some important aspects from that of a dislocation near a bimetallic interface.     

Fracture mechanics assessment of stress concentrations in incomplete fretting contacts

Life assessment of fretting fatigue has been studied for decades. Crack-analogy methods have been proposed for analyzing fretting fatigue of flat contact pairs. In the present work we re-consider the stress field near fretting contact pairs and study the feasibility of using known fracture parameters to assess incomplete fretting contact problems. Both analytical and FEM analysis reveal that the stress field near the discontinuous round corner of a friction pad, in which the round surface has been idealized without contacting the workpiece, is the same as that of crack tip. The stress field is described by the known stress intensity factors, K_I and K_II. For sticking contact these two fracture parameters are independent, whereas for the slipping contact K_II is linearly correlated with K_I. Therefore, the stress field around the slipping contact can be characterized only by one fracture parameter, together with friction coefficient. For the continuous contact pairs with finite round contact surface, the local stress concentrations near the contact edge are finite and can be characterized by K_I and K_II, either, in analogy to the blunting crack tip due to finite strains. Detailed computations confirm that using the fracture parameters to characterize the fretting contact failure is affected by both loading condition and friction pad geometry. The dominance zone around the pad corner decreases more significantly with vertical press load than the horizontal friction load. In the bi-material contact friction pair the stress field can be described by K_I and K_II in the same form.     

Edge dislocation in an anisotropic material with a surface layer

The forces of interaction between a stationary edge dislocation and a surface layer are discussed in the framework of the elastic continuum approximation. Both of the semi-infinite medium and the surface layer, which are bonded together, are assumed to be anisotropic here. The solution in Fourier integral form can be derived by using the complex stress function.Some numerical calculations are carried out for the simple case where the direction of the Burgers vector of dislocation is perpendicular to the interface. The results show that the dislocation has a stable equilibrium position near the interface for certain combination of elastic coefficients.     

A method for eliminating the effect of 3-D bi-material interface corner geometries on stress singularity

The stress singularities at three-dimensional (3-D) interface corners and edges have been investigated numerically using common finite element methods. The effects of variation of edge angle and vertex angle between the two free side surfaces on the order of stress singularity at bi-material interface corners are determined. It is found that the order of stress singularity at interface corner depends not only on the combination of materials and edge angles but also on the vertex angle between the two free side surfaces. The effect of the vertex angle on the order of stress singularity at interface corner can be eliminated by smoothing the intersection of interface edges, which can be achieved simply by generating a circular-arc fillet at the intersection of the two free side surfaces. The numerical results show that, after smoothing the intersection of interface edges, the order of stress singularity along the interface edges become continuous, i.e. the order of the corner singularity can be reduced to the level of the edge singularity.     

Comparison of elastic interaction of a dislocation and a crack for four bonding conditions of the crack plane

A comparison of elastic interaction of a dislocation and a crack for four bonding conditions of the crack plane was made. Four cases of single crystalline material, sliding grain boundary, perfectly bonded interface, and sliding interface were considered. The stress intensity factors arising from edge and screw dislocations and their image forces for the above four cases were compared. The stress intensity factor at a crack tip along the perfectly bonded interface arising from screw dislocation can be obtained from that in a single crystalline material if the shear modulus in the single crystalline material is replaced by the harmonic mean of both shear moduli in the bimaterial. The stress intensity factor at a crack tip along the sliding interface arising from edge dislocation in the bimaterial can be obtained from that along the sliding grain boundary in the single material if the μ/(1−ν) in the single material is substituted by the harmonic mean of μ/(1− ν) in the bimaterial where μ and ν are the shear modulus and Poisson's ratio, respectively. The solutions of screw dislocation near a crack along the sliding grain boundary and sliding interface are the same as that of screw dislocation and its mirror image. Generally, the effect of edge dislocation for perfectly bonded interface on the crack propagation is more pronounced than that for the sliding interface. The effect of edge dislocation on the crack propagation is mixed mode for the cases of perfectly bonded interface and single crystalline material, but mode I fracture for the cases of sliding interface and sliding grain boundary. All curves of Fx versus distance r from the dislocation at interface to the right-hand crack tip are similar to one another regardless of dislocation source for both sliding interface and perfectly bonded interface. The level of Fx for m=0 is larger than that for m=−1. This revised version was published online in August 2006 with corrections to the Cover Date.     

Application of conservation integrals to interfacial crack problems

Properties of the J, L and M integrals, proposed by Knowles and Sternberg for homogeneous materials are explored here for bi-material interfaces. The integrals are shown to satisfy the conservation law under certain conditions on the interfaces. Relations between the stress intensity factors and the conservation integrals for interfacial cracks in isotropic, linear-elastic materials are derived. The conservation integrals for some interfacial cracks are applied to get the stress intensity factors in a very simple way without solving the complicated boundary value problems. For interfacial cracks in finite-sized medium some numerical computations are carried out to verify the usefulness of the conservation integrals.     

Evaluation of first non-singular stress term in bi-material notches

The influence of the first non-singular stress term on the stress field near the bi-material notches has been evaluated. An extensive study has been carried out on the higher order eigenvalues and their correlation with the notch angle and the material combination of the bi-material joints. The coefficients of singular and non-singular terms of the stress field were then calculated for two laboratory specimens with different notch angles and material configurations of the bi-material joints using the displacement field obtained from finite element analysis. It was shown that considering only the two singular terms of a bi-material notch in order to characterize the near stress field may lead to significant errors. Adding the first non-singular term called I-stress, however, could improve the accuracy of the stresses near the notch tip efficiently. Therefore, a three-parameter model including the two singular terms and the I-stress term for predicting the onset of brittle fracture in the bi-material notched components is likely to be more accurate than the classical models which are based only on the singular terms.     

基于分子动力学模拟结果的界面破坏准则

结合材料的破坏通常都是从界面或其附近发生的,但界面破坏的机理及其评价准则尚未十分清楚。采用分子动力学模拟方法,可以对结合材料的界面起裂过程进行模拟,从而获得结合材料界面应力和界面破坏之间的关系。虽然在分子动力学模拟中采用了高度简化的界面模型,但对界面起裂过程的模拟,仍可以帮助人们获得结合材料界面破坏过程的规律性认识。通过在界面附近引入初始裂纹,导致界面上应力集中,从而引起界面起裂。从分子动力学模拟结果出发,提出了一个结合材料界面起裂,即界面破坏的准则。     

Long-range gettering of microdefects in silicon single crystals during the formation of porous silicon layers on their surface and ion irradiation

Experimental data on the dissolution of microdefects in the near-surface regions of silicon single crystals during the electrochemical formation of porous silicon layers followed by argonion irradiation are presented. A decrease in the microdefect concentration is detected near the interface with porous silicon and near the opposite surface of the samples. Pis’ma Zh. Tekh. Fiz. 25, 50–54 (April 26, 1999)     

Effect of interface layer consisting of nanosprings on stress field near interface edge

The purpose of this study is to investigate the effect of an interface layer consisting of discretely arrayed nano-sized elements on stress intensified fields. A material where an interface layer consisting of Ta₂O₅ helical nanoelements (nanosprings) is inserted between dissimilar components is prepared and two types of crack initiation experiments, which possess radically different stress conditions, are carried out. The finite element analyses indicate that the stress fields in the components with and without the interface layer are completely different, and it is experimentally clarified that the fracture mechanics concept cannot be applied to the crack initiation at the dissimilar interface edge with the interface layer. The stress distributions at the crack initiation reveal that the crack initiation is governed by the apparent stress of the nanospring, σ′, at the edge. This signifies that the interface layer eliminates the stress singular field at the interface edge. The criterion of the crack initiation is evaluated as .     

Improvement strategy for edge waviness in roll bending process of corrugated sheet metals

This paper focuses on the corrugated thin-walled sheet metal in the roll bending process. The main defect that appears in corrugated panels subjected to high amounts of bending deformation is a wavy edge. Edge defects are caused by excessive longitudinal stress and strain near the edge of the plate, and local edge buckling may occur when some critical value of the bending radius is exceeded. This paper proposes two different approaches to avoid a wavy edge for a formed panel: excessive stress on the edge region is restrained by controlling the length of the cross-sectional end of the corrugated panel while considering the stress distribution, and the bending radius in each forming step is determined by considering the strain limit at which the initial edge waviness occurs to avoid excessive compression at particular steps. The experimental and numerical results indicated that the two proposed design strategies can minimize wavy edges in the formed shape.