scholarly journals On Interlaminar Failure due to Mechanical and Thermal Stresses at the Free Edges of Composite Laminated Plates

1994 ◽  
Vol 3 (5) ◽  
pp. 096369359400300
Author(s):  
S. K. Morton ◽  
J. P. H. Webber
Keyword(s):  
Stress Field ◽  
Analytical Model ◽  
Thermal Stresses ◽  
Three Dimensional ◽  
Free Edge ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Composite Laminated Plate ◽  
Composite Laminated Plates ◽  
Thermoelastic Effects

The three-dimensional stress field that occurs near a free edge in a composite laminated plate may lead to interlaminar failure. On the basis of an analytical model for this stress field, critical applied loads for interlaminar failure are predicted using a quadratic criterion. Both mechanical and thermoelastic effects are considered.

Approximate Design Analysis of Failure Within Composite Laminated Plates

1982 ◽  
Vol 104 (3) ◽  
pp. 604-611 ◽  
Author(s):  
R. L. Gallo ◽  
A. N. Palazotto
Keyword(s):  
Computer Simulation ◽  
Analytical Study ◽  
Three Dimensional ◽  
Free Edge ◽  
Laminated Plates ◽  
Curing Temperature ◽  
Laminated Plate ◽  
Approximate Design ◽  
Composite Laminated Plates ◽  
Good Agreement

This paper is an analytical study of the effects of interlamina stresses near the free edge of a laminated plate due to axial and moment loading variations. A three-dimensional extension of the Tsai-Hill failure criterion is introduced to predict delamination. Results achieved by computer simulation show good agreement with experimental observations made by other sources. The distance from the free edge is decidedly important as is the effect of curing temperature because of the consequences these parameters have on the magnitude of the stress field. The failure estimations provide an approximate bound and are worthy of due consideration by the design engineer in the stress analysis of test specimens.

Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

2017 ◽  
Vol 9 (6) ◽  
pp. 1485-1505
Author(s):  
Lingchang Meng ◽  
Fengming Li
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Composite Laminated Plate ◽  
Vibration Localization ◽  
Composite Laminated Plates ◽  
Localization Phenomenon ◽  
Harmonic Resonance

AbstractThe nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.

Nonlinear Vibration Behaviors of Composite Laminated Plates with Time-Dependent Base Excitation and Boundary Conditions

2017 ◽  
Vol 18 (2) ◽  
Author(s):  
Yu-Yang Chai ◽  
Feng-Ming Li ◽  
Zhi-Guang Song
Keyword(s):  
Boundary Conditions ◽  
Theoretical Method ◽  
Laminated Plates ◽  
Time Dependent ◽  
Laminated Plate ◽  
Base Excitation ◽  
Analysis And Design ◽  
Composite Laminated Plate ◽  
Composite Laminated Plates ◽  
Frequency Relationship

AbstractThe nonlinear vibrations of composite laminated plates with time-dependent base excitation and boundary conditions are investigated. According to the von Kármán nonlinear plate theory, the dynamic equations of motion of the laminated plates are established. The nonlinear partial differential equations are transformed to the nonlinear ordinary differential ones using the Bubnov-Galerkin’s  method. The primary resonance and the primary parametric resonance of the laminated plate with time-dependent boundary conditions are investigated by means of the method of multiple scales. The validity of the present theoretical method is verified by comparing the amplitude–frequency relationship curves acquired from the present theoretical method with those calculated from the numerical simulation. The amplitude–frequency characteristic curves and the displacement time histories for different ply angles of the composite laminated plate are analyzed. The effects of the viscous damping factor and the transverse displacement excitation on the amplitude–frequency relationship curves are also studied. The present results are helpful for the nonlinear dynamical analysis and design of the composite laminated plate with time-dependent boundary conditions.

Interfacial Thermal Stresses in Layered Structures: The Stepped Edge Problem

1995 ◽  
Vol 117 (2) ◽  
pp. 153-158 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Stress Field ◽  
Elastic Layer ◽  
Thermal Stresses ◽  
Free Edge ◽  
Multilayered Structure ◽  
Local Geometry ◽  
Temperature Load ◽  
Edge Problem ◽  
Stress Functions ◽  
Multilayer Substrate

The intense, localized stress field produced by a temperature load in a multilayered structure may be significantly affected by the local geometry of the free edge. We examine here the stepped edge problem associated with bonding an elastic layer (silicon chip) to a single or multilayer substrate with a slightly larger length. Stress functions are introduced in various rectangular regions and the continuity of tractions are enforced across all inter-region boundaries. Furthermore, continuity of displacements is enforced across the junction of the two segments of the base laminate. The analysis results indicate that even a minute protrusion of the edge of the base laminate relative to the attached chip may cause significant changes in the peeling and shearing stresses in the end region of the interface.

Evaluation of the Bonding Strength at the Three-Dimensional Vertex in Silicon-Resin Joints

2009 ◽  
Author(s):  
Hideo Koguchi ◽  
Masato Nakajima
Keyword(s):  
Stress Distribution ◽  
Stress Field ◽  
Boundary Element ◽  
External Force ◽  
Thermal Stresses ◽  
Three Dimensional ◽  
Singular Stress ◽  
Singular Stress Field ◽  
Element Method ◽  
Silicon Resin

Portable electric devices such as mobile phone and portable music player become compact and also their performance improves. High density packaging technology such as CSP (Chip Size Package) and Stacked-CSP is needed to realize advanced functions. CSP is a bonded structure composed of materials with different properties. A mismatch of material properties may cause stress singularity at the edge of interface, which lead to the failure of bonding part in structures. Singular stress field in residual thermal stresses occurs in a cooling process after bonding the joints at a high temperature. In the present paper, the strength of interface in CSP consisted of silicon and resin is investigated. Boundary element method and an eigen value analysis based on finite element method are used for evaluating the intensity of singularity of residual thermal stresses at a vertex in a three-dimensional joint. Three-dimensional boundary element program based on the fundamental solution for two-phase isotropic body is used for calculating the stress distribution in the three-dimensional joint. Angular function in the singular stress field at the vertex in the three-dimensional joint is calculated using eigen vector determined from eigen analysis. The strength of bonding at the interface in several silicon-resin specimens with different thickness of resin is investigated analytically and experimentally. Stress singular analysis applying an external force for the joints is firstly carried out. After that, singular stress field for the residual thermal stresses varying material property of resin with temperature is calculated. Combining singular stress fields for the external force and the residual thermal stress yields a final stress distribution for evaluating the strength of interface. A relationship between the external force for delamination in joints and the thickness of resin is derived. Finally, a critical intensity of singularity for delamination between silicon and resin is determined.

Multiterm Extended Kantorovich Method for Three-Dimensional Elasticity Solution of Laminated Plates

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
Santosh Kapuria ◽  
Poonam Kumari
Keyword(s):  
Stress Field ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Laminated Plates ◽  
Elasticity Solution ◽  
Kantorovich Method ◽  
Extended Kantorovich Method ◽  
Single Term ◽  
3D Elasticity ◽  
Laminated Structures

In an article recently published in this journal, the powerful single-term extended Kantorovich method (EKM) originally proposed by Kerr in 1968 for two-dimensional (2D) elasticity problems was further extended by the authors to the three-dimensional (3D) elasticity solution for laminated plates. The single-term solution, however, failed to predict accurately the stress field near the boundaries; thus limiting its applicability. In this work, the method is generalized to the multiterm solution. The solution is developed using the Reissner-type mixed variational principle that ensures the same order of accuracy for displacements and stresses. An n-term solution generates a set of 8n algebraic-ordinary differential equations in the in-plane direction and a similar set in the thickness direction for each lamina, which are solved in close form. The problem of large eigenvalues associated with higher order terms is addressed. In addition to the composite laminates considered in the previous article, results are also presented for sandwich laminates, for which the inaccuracy in the single-term solution is even more prominent. It is shown that considering just one or two additional terms in the solution (n = 2 or 3) leads to a very accurate prediction and drastic improvement over the single-term solution (n = 1) for all entities including the stress field near the boundaries. This work will facilitate development of near-exact solutions of many important unresolved problems involving 3D elasticity, such as the free edge stresses in laminated structures under bending, tension and torsion.

Constitutive Relations for Fiber-Reinforced Inelastic Laminated Plates

1984 ◽  
Vol 51 (1) ◽  
pp. 107-113 ◽  
Author(s):  
J. Aboudi ◽  
Y. Benveniste
Keyword(s):  
Stress Field ◽  
Effective Stress ◽  
Strain Field ◽  
Constitutive Relations ◽  
Laminated Plates ◽  
Constitutive Behavior ◽  
Laminated Plate ◽  
Fiber Reinforced ◽  
Cylindrical Bending ◽  
Legendre Expansion

Effective stress-strain relations for inelastic unidirectional composites developed previously are used to derive the gross constitutive behavior of inelastic laminates in which every lamina is fiber-reinforced. The laminated plate is subjected to stretching and bending deformation and the strain field is described by the Love-Kirchhoff hypothesis. The distribution of the resulting stresses across the thickness is necessarily nonlinear and a Legendre expansion formalism is used to determine the stress field. Results are given for cross-ply symmetric laminates under pure cylindrical bending.

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