A precise and efficient method for evaluating singular stress field at the vertex in three dimensional bonded body

In this paper, convenient analysis methods are proposed for analyzing the singular index and the intensity of singular stress field (ISSF) at the vertex on the interface in the three dimensional (3D) bonded body. The analysis methods focus on FEM stresses at and around the vertex. The singular index is determined from the FEM stress ratio at the vertex obtained by performing FEM analyses for the finely and coarsely meshed models. Then, the ISSF is determined from the average FEM stresses around the vertex obtained for the reference and unknown models by applying the similar mesh pattern. The validity of the present methods is examined by comparing the results of 3D bonded models with/without fixed free surfaces. It is found that the obtained singular index has the same accuracy as the FEM eigenvalue analysis. The asymptotic solutions with the singular index and ISSF obtained by the present method correspond to FEM stress distributions. Since the ISSF obtained by the body force method (BFM) is used as the reference solution, the present method for ISSF has the same accuracy as BFM. Moreover, the critical ISSF values are calculated from the experimental results of the butt joints under various adhesive thicknesses. The critical ISSF at the side of 3D butt joint is in good agreement with the critical ISSF of 2D butt joint model. It is shown that the critical ISSF at the vertex of 3D joint is constant as well as the critical 2D ISSF independent of the adhesive thickness.

[1]  F. Ren,et al.  Validity of the Adhesive Strength Evaluation Method Based on the Intensity of Singular Stress Field in Two-Dimensional Modelling , 2018, Journal of The Japan Institute of Electronics Packaging.

[2]  N. Noda,et al.  Debonding strength evaluation in terms of the intensity of singular stress at the interface corner with and without fictitious crack , 2015 .

[3]  Y. Zhang,et al.  Corrigendum to “A mesh-independent technique to evaluate stress singularities in adhesive joints” [Int. J. Adhes. Adhes. 57(2015) 105–117] , 2015 .

[4]  Y. Zhang,et al.  A mesh-independent technique to evaluate stress singularities in adhesive joints , 2015 .

[5]  N. Noda,et al.  Intensity of Singular Stress at the End of a Fiber under Pull-Out Force , 2007 .

[6]  I. R. Pashby,et al.  Joining techniques for aluminium spaceframes used in automobiles , 2000 .

[7]  I. Ihara,et al.  Analysis for Stress Singularity Field at a Vertex in Three-Dimensional Bonded Structures. , 1999 .

[8]  Alfred Rotimi Akisanya,et al.  An experimental investigation of failure initiation in bonded joints , 1998 .

[9]  S. Pageau,et al.  Finite element evaluation of free-edge singular stress fields in anisotropic materials , 1995 .

[10]  S. Pageau,et al.  The order of stress singularities for bonded and disbonded three-material junctions , 1994 .

[11]  Yasuaki Suzuki,et al.  Adhesive Tensile Strengths of Scarf and Butt Joints of Steel Plates (Relation Between Adhesive Layer Thicknesses and Adhesive Strengths of Joints) : Solid-Mechanics, Strength of Materials , 1987 .

[12]  David B. Bogy,et al.  Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading , 1968 .

[13]  N. Noda,et al.  A Precise and Efficient Analytical Method to Obtain Two Distinct Intensities of Singular Stress Fields for Single Lap Joint , 2018 .

[14]  F. Ren,et al.  Intensity of Singular Stress Field Distributions along interface for 3D Butt Joint , 2017 .

[15]  N. Miyazaki,et al.  Development of the singular stress analyses for three-dimensional interfacial corners , 2017 .

[16]  T. Kurahashi,et al.  Evaluation of stress singularity field near vertex on interface of dissimilar material joints based on Akin singular element using three-dimensional order of singularity (Comparison of results in case of tetrahedron and singular elements) , 2014 .

[17]  N. Noda,et al.  Convenient Debonding Strength Evaluation Based on the Intensity of Singular Stress for Adhesive Joints , 2014 .

[18]  Yasuaki Naito,et al.  Dissimilar Metal Joining Technologies for Steel Sheet and Aluminum Alloy Sheet in Auto Body , 2013 .

[19]  N. Noda,et al.  Debonding Criterion for Single Lap Joints from the Intensity of Singular Stress Field , 2013 .

[20]  Toshiyuki Sawa,et al.  Recent Researches on Stress Analysis of Adhesive Joints and Future Issues to be Examined , 2009 .

[21]  H. Sakai,et al.  Analysis of Stress Singularity Field in Three-Dimensional Joints Using Three-Dimensional Boundary Element Method , 2005 .

[22]  Alfred Rotimi Akisanya,et al.  Initiation of fracture at the interface corner of bi-material joints , 2003 .

[23]  Dai-heng Chen,et al.  Intensity of Singular Stress Field near the Interface Edge Point of a Bonded Strip. , 1993 .

[24]  J. Dundurs,et al.  Discussion of Edge-Bonded Dissimilar Orthogonal Elastic Wedges under Normal and Shear Loading , 1969 .