Free-edge Stress Singularity Research Articles

The influence of the first non-singular stress terms on crack initiation direction in an orthotropic bi-material plate

A bi-material plate composed of two orthotropic parts leads to free edge stress singularity. This is considered as a bi-material notch with ω1=ω2=90° under general loading. Besides the singular term the first non-singular term is also included in the stress distribution at the notch tip. The Stroh–Eshelby–Lekhnitskii formalism for plane elasticity is used to express stress and displacement fields and the strain energy density factor. The exponents of the singular and non-singular stress terms and corresponding eigenvectors are the solution of the eigenvalue problem resulting from the prescribed boundary and compatibility conditions at the notch tip. The potential direction of crack initiation is determined from the local minimum of the mean value of the strain energy density factor in both materials. The necessary knowledge of the generalized stress intensity factor and generalized T-stress is realized by means of the employment of the two state conservation integrals. Following the assumption of the same mechanism of rupture in the case of a crack and a notch, an expression for the critical values of the generalized stress intensity factor is obtained.

中間層を有する異種接合材の熱応力負荷下での応力特異性

Free-edge stress singularity usually develops near the edge of interface of bonded dissimilar materials. Because of the difference of the coefficient of the thermal expansion of the materials, the residual stress may develop when two materials are bonded. To defuse the residual stress, an interlayer may be inserted between the two materials. Stress distribution near the edge of the interface in the presence of the interlayer is very important to evaluate the strength of the bonded dissimilar materials. In this study, stress distribution on the interfaces of the bonded dissimilar materials with an interlayer under thermal stress loading was calculated by using the boundary element method. An effect of an interlayer on the stress distributions on the interface was examined numerically. It was found that the influence of the interlayer on the stress distribution was limited within a region where distance from interface edge is smaller than the interlayer thickness. Stress distribution around the edge of the interface of the bonded dissimilar materials with an interlayer can be normalized by the parameters of the singularity and the thermoelastic constant stress term of the bonded dissimilar materials without an interlayer.

Stress concentration/intensity around elliptical/circular cylinder shaped surface flaws in cross-ply plates and validity of St. Venant’s principle in the presence of interacting singularities

Effects of localized elliptical (circular being a special case) cylindrical surface flaws in laminated composite plates are investigated by using C°-type triangular composite plate elements, formulated on the assumptions of transverse inextensibility and layer-wise constant shear-angle theory (LCST). Numerical results for a cross-ply laminate compromised by the presence of an external part-through elliptical/circular cylindrical slot indicate the existence of severe cross-sectional warping in the vicinity of the surface flaw and plate boundaries. Furthermore, three-dimensional nature of the stress concentration factor in the neighborhood of the elliptical or circular cylinder shaped surface flaw boundary is clearly exhibited. Besides, very high stress concentration factors are found in the layer weakened by the surface flaw. Most importantly, the effects of stress singularity in the neighborhood of the circumferential re-entrant corner lines of the elliptical/circular cylindrical surface flaws, weakening laminated composite plates, are numerically assessed, because of their role in crack initiation. Finally, the interaction of this singularity with free edge stress singularity at the plate boundary, and the implication of such interactions (i.e., violation of St. Venant’s principle) in regards to testing of laminated composite specimens are thoroughly investigated.

直交異方性異種接合材の界面端に生じる対数関数型応力特異性

When two materials are bonded, free-edge stress singularity usually develops at the intersection of free-surfaces and interface. The order of the free-edge stress singularity p can be obtained as a root of the characteristic equation deduced in terms of Airy's stress function. It is theoretically predicted that logarithmic free-edge singularity develops when the order of the singularity p has double root, but no numerical examination is available in the literature. In this study, stress distribution on the interface of the bonded dissimilar orthotropic materials is calculated by using the boundary element method (B.E.M.) under the condition where the order of the singularity has the double root of the characteristic equation. It was found that the logarithmic free-edge stress singularity developed under mechanical loading. The order of the stress singularity calculated by the nonlinear least squares method from the stress distribution obtained by B.E.M. analyses agreed well with one obtained by using the characteristic equation. The logarithmic free-edge stress singularity developed under thermal stress loading also.

OS0808 任意の主軸方向を有する直交異方性異材の接合界面端応力特異性の発生・消失に関する検討(OS8-2 接合界面・接着,OS-8 機械の接合部・接触部のプロセスと疲労・強度問題2)

OS0808 任意の主軸方向を有する直交異方性異材の接合界面端応力特異性の発生・消失に関する検討(OS8-2 接合界面・接着,OS-8 機械の接合部・接触部のプロセスと疲労・強度問題2)

612 任意の主軸方向を有する直交異方性異種接合材の自由縁応力特異性に関する理論的検討(GS-3破壊力学・材料じん性)

612 任意の主軸方向を有する直交異方性異種接合材の自由縁応力特異性に関する理論的検討(GS-3破壊力学・材料じん性)

320 直交異方性異種接合材料に対して界面端特異性を消失させる中間層の材料定数選定に関する理論的および数値的検討(GS-4 異種接合)

320 直交異方性異種接合材料に対して界面端特異性を消失させる中間層の材料定数選定に関する理論的および数値的検討(GS-4 異種接合)

1408 直交異方性異種接合材料の界面端応力特異性の発生・消失の判定手法に関する検討(OS14-2 締結・接合部のプロセスと信頼性評価-接着接合-)

1408 直交異方性異種接合材料の界面端応力特異性の発生・消失の判定手法に関する検討(OS14-2 締結・接合部のプロセスと信頼性評価-接着接合-)

Free-Edge Stress Singularity of Bonded Dissimilar Materials with an Interlayer

Free-edge stress singularity usually prevails at the edge of the interface of the bonded dissimilar materials. When two materials are bonded by using an adhesive, an interlayer develops between two materials. An interlayer may inserted between two materials to defuse the residual stress due to the difference in the coefficients of thermal expansion. In this study, to investigate the effect of the interlayer on the free-edge stress singularity of the bonded dissimilar materials with an interlayer, the stress distributions on the interface were examined numerically and theoretically. Relation between the free-edge stress singularity of the bonded dissimilar materials with and without an interlayer was investigated by using the boundary element method. It was found that the effect of the interlayer on the stress distribution was limited within a small area of the order of the interlayer thickness. Stress distributions near the edge of the interface were controlled by the free-edge stress singularity of the bonded dissimilar materials without an interlayer.

Singular stress field near the edge of interface of bonded dissimilar materials with an interlayer

For bonded dissimilar materials, the free-edge stress singularity usually prevails near the intersection of the free-surface and the interface. When two materials are bonded by using an adhesive, an interlayer develops between the two bonded materials. When a ceramic and a metal are bonded, the residual stress develops because of difference in the coefficient of thermal expansion. An interlayer may be inserted between the two materials to defuse the residual stress. Stress field near the intersection of the interface and free-surface in the presence of the interlayer is then very important for evaluating the strength of bonded dissimilar materials. In this study, stress distributions on the interface of bonded dissimilar materials with an interlayer were calculated by using the boundary element method to investigate the effect of the interlayer on the stress distribution. The relation between the free-edge singular stress fields of bonded dissimilar materials with and without an interlayer was investigated numerically. It was found that the influence of the interlayer on the stress distributions was confined within a small area of the order of interlayer thickness around the intersection of the interface and the free-surface when the interlayer was very thin. The stress distribution near the intersection of the interface and the free-surface was controlled by the free-edge stress singularity of the bonded dissimilar materials without the interlayer. In this case, the interlayer can be called free-edge singularity-controlled interlayer. If a stress distribution on the interface is known for one thickness of an interlayer h, stress distributions on the interface for other values of h can be estimated.

528 直交異方性異材接合界面への中間層挿入による界面端特異性の消失に関する数値的検討(GS.B 接着・接合)

The free-edge stress singularity usually prevails at the edge of the interface of the bonded dissimilar materials. Anisotropic materials are often used to make a bonded dissimilar materials. When two materials are bonded, an interlayer may be inserted between two materials. In this study, free-edge stress singularity of bonded dissimilar orthotropic materials with an interlayer was investigated by using the boundary element method. It was found that the free-edge stress singularity disappeared by inserting a proper material between the bonded dissimilar materials which has a free-edge stress singularity at the edge of interface.

Free-Edge Singular Stress Field of Bonded Dissimilar Materials with an Elastic-Plastic Interlayer

In this study, stress distributions on the interface of bonded dissimilar materials with an elastic-plastic interlayer were calculated by using the finite element method and the effect of the elastic-plastic interlayer on the free-edge stress singularity was investigated. It was found that the free-edge stress singularity varied with applied load in the elastic-plastic case. Stress distribution near the intersection of the free-surface and the interface was controlled by the free-edge stress singularity of the bonded dissimilar materials without interlayer as in the case of elastic analyses. Stress distribution near the intersection of the free-surface and the interface normalized considering the free-edge stress singularity can be expressed by a function of the distance from the edge of interface normalized by the thickness of interlayer. The normalized stress distribution can be used to estimate stress distributions for other values of interlayer thickness.

Convex interfacial joints with least stress singularities in dissimilar materials

An integrated experimental and numerical investigation is employed to evaluate a new axisymmetric convex joint for the least free-edge stress singularity. Quasi-static tension and dynamic tension experiments of both straight and convex bi-material joints are conducted. Experimental results show that the convex joint yields an increase in final failure strength (up to 22%) and a reduction in material volume (at least 18%), compared to the traditional straight-edged joint. Finite element results indicate that the new axisymmetric convex interfacial joint is effective in removing the stress singularity at the bi-material edge and consequently, a relatively uniform interfacial stress distribution is achieved. The uniform stress distribution leads to more reasonable interfacial strength measurements and higher tensile strengths of dissimilar material joints.

3234 直交異方性異種接合材の自由縁特異応力場への中間層の影響(J07-2 締結・接合の力学とプロセス(2),J07 締結・接合の力学とプロセス)

The free-edge stress singularity usually develops near the edge of the interface of the bonded dissimilar materials. Anisotropic materials may be used for making bonded dissimilar materials. When two materials are bonded, an interlayer, for example an adhesive layer, may be inserted between two materials. In this study, free-edge stress singularity of bonded dissimilar orthotropic materials with an interlayer was investigated by using the boundary element method. It was found that the influence of the interlayer on the stress distribution on interface was limited in the region of the order of the interlayer thickness around the edge of interface similar to the bonded dissimilar isotropic materials. Free-edge stress singularity disappeared by inserting a proper materials between the bonded dissimilar materials.

Free-Edge Stress Singularity in Bonded Dissimilar Orthotropic Materials Under Thermal Stress Leading

When two dissimilar materials are bonded, thermal stresses develop due to the difference in coefficient of thermal expansion of the materials. In recent years, not only isotropic materials but also anisotropic materials are used for making bonded dissimilar materials. In this study, free-edge stress singularity of bonded dissimilar orthotropic materials under thermal stress loading is investigated theoretically. The thermal stresses show the free-edge stress singularity similar to that under mechanical loading, when the thermoelastic constant stress term is subtracted. Stress distributions on the interface are calculated by using the boundary element method. The value of the order of thermal stress singularity determined by using boundary element results agrees well with the theoretical value obtained by using the characteristic equation. It is shown that the thermal stress singularity disappears for certain ranges of wedge angles of a pair of materials.

Theoretical and Numerical Study on Disappearance of Free-Edge Stress Singularity by Inserting an Interlayer to Bonded Dissimilar Materials

The free-edge stress singularity usually develops near the intersection of the free-surface and the interface for the bonded dissimilar materials. When two materials are bonded by using an adhesive, an adhesive layer may develop between two bonded materials. To defuse the residual stress which develops because of the difference of the coefficient of thermal expansion, an interlayer may be inserted between two materials. On the other hands, the free-edge stress singularity disappears for certain pair of materials. In this study, the disappearance of free-edge stress singularity by inserting the interlayer to the bonded dissimilar materials for which free-edge stress singularity develops were investigated theoretically and numerically. It was found that the free-edge stress singularity disappeared by inserting a proper material to the bonded dissimilar materials. It was theoretically shown that there existed combination of material parameters of such an interlayer. Stress distributions on the interface of bonded dissimilar materials with an interlayer were calculated by using the boundary element method, and disappearance of free-edge stress singularity was confirmed numerically. When the interlayer was very thin, stress distribution near the intersection of the interface and free-surface was controlled by the free-edge stress singularity of the bonded dissimilar materials without the interlayer.

926 弾性および弾塑性解析による中間層が存在する異種接合材の界面端近傍特異応力場に関する検討(GS-3,4 環境・破壊,研究発表講演)

926 弾性および弾塑性解析による中間層が存在する異種接合材の界面端近傍特異応力場に関する検討(GS-3,4 環境・破壊,研究発表講演)

319 中間層を有する異種接合材の界面端特異応力場の弾塑性解析(GS9 応力解析43)

319 中間層を有する異種接合材の界面端特異応力場の弾塑性解析(GS9 応力解析43)

Dissimilar material joints with and without free-edge stress singularities: Part I. A biologically inspired design

An integrated experimental and numerical investigation was conducted for removing the free-adge stress singularities in dissimilar material joints. A convex inter-face/joint design, inspired by the shape and mechanics of trees, will result in reduced stress singularities at bimaterial corners for most engineering material combinations.In situ photoelasticity experiments on convex polycarbonate-aluminum joints showed that the free-edge stress singularity was successfully removed. As a result, the new design not only improves the static load transfer capacity of dissimilar meterial joints, but also yields more reasonable interfacial tensile strength evaluation. For convex polycarbonate-aluminum and poly(methyl methacrylate)-aluminum joint specimens, the ultimate tensile load increased up to 81% while the total material volume was reduced by at least 15% over that of traditional butt-joint specimens with severe free-edge stress singularities.

Relation between Stress Intensity Factor of a Small Edge Interface Crack and Intensity of Free-Edge Stress Singularity of Bonded Dissimilar Materials

When two materials are bonded, the free-edge stress singularity usually develops near the intersection of the interface and the free-surface. Fracture in bonded dissimilar materials may therefore occur from an interface crack which develops at the intersection of interface and free-surface. Free-edge stress singularity is very important in the evaluation of strength of bonded dissimilar materials. In this study, the relationship between the stress intensity factor of a small edge crack on interface of bonded dissimilar materials and the intensity of free-edge stress singularity of bonded dissimilar materials with no crack under external mechanical loading was investigated numerically by using the boundary element method. The relationship was also investigated theoretically by using the principle of superposition. The results of numerical analyses were compared with those of theoretical analyses. It was found that stress intensity factors of small edge crack on interface K1 and K2 were proportional to the intensity of free-edge stress singularity of bonded dissimilar materials Kσ without crack irrespective of the combination of materials. The numerically determined proportional coefficient between K1 and Kσ agreed well with the theoretical one, and was not affected by crack length when proper normalizations were applied. From these results, it is suggested that stress intensity factor of small edge crack on interface can be used as a strength criterion of interface of bonded dissimilar materials.