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.

The Effects of Inclined Free Edges on the Thermal Stresses in a Layered Beam

1993 ◽  
Vol 115 (2) ◽  
pp. 208-213 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Thermal Stresses ◽  
Stress Singularity ◽  
Approximate Solutions ◽  
Free Edge ◽  
Local Concentration ◽  
Interlaminar Stresses ◽  
Beneficial Effects ◽  
Stress Functions ◽  
Layered Beam ◽  
Free Edges

A stress-function-based variational method is used to determine the thermal stresses in a layered beam with inclined free edges at the two ends. The stress functions are expressed in terms of oblique cartesian coordinates, and polynomial expansions of the stress functions with respect to the thickness coordinate are used to obtain approximate solutions. Severe interlaminar stresses act across end segments of the layer interfaces. Local concentration of such stresses may be significantly affected by the inclination angle of the end planes. Variational solutions for a two-layer beam show generally beneficial effects of free-edge inclination in dispersing the concentration of interlaminar stresses. The significance of these effects is generally not indicated by the power of the stress singularity as computed from an elasticity analysis of a bimaterial wedge.

Thermal Stress in a Coated Short Fibre Composite

1986 ◽  
Vol 53 (3) ◽  
pp. 681-689 ◽  
Author(s):  
Yozo Mikata ◽  
Minoru Taya
Keyword(s):  
Stress Field ◽  
Thermal Stresses ◽  
Fibre Composite ◽  
Extreme Case ◽  
Short Fibre ◽  
Thermal Expansion Coefficients ◽  
Stress Functions ◽  
Expansion Coefficients ◽  
Short Fibre Composite ◽  
Good Agreement

When a coated short fibre composite is subjected to temperature change, thermal stresses in and around the coated fibres are induced due to the mismatch of thermal expansion coefficients of the constituents, resulting in a possibility of cracking in the coating. The problem of the above thermal stresses in a coated short fibre composite is solved by using the Boussinesq-Sadowsky stress functions. The present results are compared with Eshelby’s solutions for an extreme case and good agreement between the two methods is obtained. A parametric study is then conducted to examine the effect of the geometry and thermo-mechanical properties of the coating on the stress field in and around a coated short fibre. It is found in this study that the stress field in the coating is sensitive to the properties and geometry of the coating.

Refined Variational Solutions of the Interfacial Thermal Stresses in a Laminated Beam

1992 ◽  
Vol 114 (2) ◽  
pp. 193-198 ◽  
Author(s):  
W.-L. Yin
Keyword(s):  
Thermal Stresses ◽  
Virtual Work ◽  
Free Edge ◽  
Interlaminar Stresses ◽  
Laminated Beam ◽  
Variational Solutions ◽  
Stress Functions ◽  
Polynomial Expansions ◽  
Resultant Forces ◽  
Derivatives Of

Efficient and accurate solutions of the interlaminar stresses in a layered beam under a temperature loading are obtained by a variational method using stress functions and the principle of complementary virtual work. Polynomial expansions of the fifth or lower degrees are used to approximate the variation of the stress functions in the thickness direction of each layer. Comparison of the solutions of the various orders with the existing numerical and analytical solutions indicates that the variational solutions converge rapidly as the degree of the polynomial expansion increases and that even the lowest-order variational solutions yield satisfactory results for the interlaminar stresses. Over short segments of the interface adjacent to the free edge, the resultant forces of the interlaminar normal and shearing stresses are given by the first-order derivatives of the stress functions. These global measures of the severity of interlaminar peeling and shearing action are predicted accurately by the lowest-order variational solution.

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.

Thermal Stresses and Free-Edge Effects in Laminated Beams: A Variational Approach Using Stress Functions

1991 ◽  
Vol 113 (1) ◽  
pp. 68-75 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Edge Effects ◽  
Degrees Of Freedom ◽  
Thermal Stresses ◽  
Virtual Work ◽  
Free Edge ◽  
Interlaminar Stresses ◽  
Equilibrium Equations ◽  
Laminated Beam ◽  
Stress Functions ◽  
Cubic Polynomial

A variational method involving stress functions is used to determine the interlaminar stresses and the free-edge effects in a laminated beam under a temperature loading. The stress function in each layer is approximated by a cubic polynomial function of the thickness coordinate. The equilibrium equations, the traction boundary conditions, and the continuity conditions of the interlaminar stresses are exactly satisfied in this analysis, while the compatibility equations and interfacial continuity of the tangential strains are enforced in an averaged sense by applying the principle of complementary virtual work. The method is highly efficient and accurate. A thermal stress analysis for a three-layer beam using only eight eigenfunctions yield results that are comparable in accuracy to finite-element solutions involving thousands of degrees of freedom.

Analysis of Thermal Stresses and Residual Stress Changes in Railroad Wheels Caused by Severe Drag Braking

1977 ◽  
Vol 99 (1) ◽  
pp. 18-23 ◽  
Author(s):  
M. R. Johnson ◽  
R. E. Welch ◽  
K. S. Yeung
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Yield Point ◽  
Thermal Stresses ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Residual Stress Field ◽  
Thermal Stress Field ◽  
Stress Changes ◽  
Railroad Wheels

A finite-element computer program, which takes into consideration nonlinear material behavior after the yield point has been exceeded, has been used to analyze the thermal stresses in railroad freight car wheels subjected to severe drag brake heating. The analysis has been used with typical wheel material properties and wheel configurations to determine the thermal stress field and the extent of regions in the wheel where the yield point is exceeded. The resulting changes in the residual stress field after the wheel has cooled to ambient temperature have also been calculated. It is shown that severe drag braking can lead to the development of residual circumferential tensile stresses in the rim and radial compressive stresses in the plate near both the hub and rim fillets.

General Solutions of the Equations of Elasticity and Consolidation for a Porous Material

1956 ◽  
Vol 23 (1) ◽  
pp. 91-96
Author(s):  
M. A. Biot
Keyword(s):  
Stress Field ◽  
Porous Material ◽  
Elastic Material ◽  
Displacement Field ◽  
Theory Of Elasticity ◽  
Isotropic Case ◽  
General Solutions ◽  
General Properties ◽  
Stress Functions

Abstract Equations of elasticity and consolidation for a porous elastic material containing a fluid have been previously established (1, 5). General solutions of these equations for the isotropic case are developed, giving directly the displacement field or the stress field in analogy with the Boussinesq-Papkovitch solution and the stress functions of the theory of elasticity. General properties of the solutions also are examined and the viewpoint of eigenfunctions in consolidation problems is introduced.

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