Effect of thermal residual stress on the crack path in adhesively bonded joints

Mode I fracture behaviour of adhesively bonded double and cantilever beam (DCB) compact tension (CT) joints was studied using a rubber-modified epoxy (Araldite® GY260) as the adhesive. Adherends were prepared from a carbon fibre (CF)/epoxy composite or aluminium alloys. The crack path in the joints was studied based on the sign of the non-singularT-stress ahead of the crack tip by calculating the thermal residual stress in the joints using finite element analysis. The results indicate that the type of adherend materials influence the level of the thermal residual stress in the adhesive layer, which consequently causes different crack paths in the joints, i.e. a uniformly smooth fracture surface in both CT and DCB aluminium joints and a wavy crack growth in the DCB CF/epoxy composite joints. However, the fracture energies of different types of adhesive joints were almost identical to each other for bond thicknesst<0.2 mm, and a somewhat higher fracture resistance was obtained for the CF/epoxy DCB joints with large bond thickness.     

Effect of a graded interlayer on the stress intensity factor of cracks in a joint under thermal loading

In a bimaterial joint with and without a graded interlayer, the stress intensity factor of cracks perpendicular to the interface was calculated for a thermal loading by a homogeneous change in the temperature. In joints without an interlayer, the stress intensity factor increases to infinity as the crack approaches the interface for the case of the Young’s moduli E₁/E₂>1 (crack in material 1). Introducing a graded interlayer with a continuous transition in the material properties between the two joined materials leads to a continuous change in the stress intensity factor if the crack propagates from material 1 into material 2. Results are presented for different transition functions of the material properties and for different thickness ratios of the layers. The possible beneficial effect of a graded interlayer is discussed.     

Identification of non uniform thermal contact resistance in automated tape placement process

In this work focussing on the thermal modeling of the automated tape placement process applied to thermoplastic material, we study the thermal properties of the ply interfaces during in-situ consolidation. Through the comparison of experimental measurements and numerical simulations, we show that it is necessary to consider the existence of an interply thermal contact resistance (TCR). Furthermore, we show that in order to correctly predict the measured temperatures, the value of the thermal resistance has to evolve along the process although a very simple evolution law is sufficient.     

Effect of transformation temperature range on generation of thermal stress and strain during quenching

Abstract

Composition varies sufficiently widely within an alloy specification to allow significant variations in the temperature ranges within which the austenite phase transforms to martensite. It has been suggested that such variations in composition are associated with anomolous fluctuations in the distortions produced in quenched components of a particular alloy. In the present work, a plane stress infinite plate mathematical model was used to conduct a quantitative examination of the connection between these compositional variations, the associated changes in the M_s and M_f temperatures, and the amount of residual stress and strain after quenching. The residual strains at the end of a water quench increased substantially as the M_s temperature increased. However, the corresponding stresses after the same water quench and both the residual stresses and strains at the end of an oil quench were only slightly affected by such changes in the M_s temperature. This displacement in the temperature range within which transformation occurred reduced the absolute value of the transformation strain, one of the components contributing to total strain. At the end of the quench the sum of the other strain components was positive and larger than the negative transformation strain, so the reduction in the absolute value of the latter, associated with the increase in the M_s temperature, led to the increase in the residual strain at the end of the quench. The results obtained support the suggestion that the limitations of fluctuations in composition within the alloy specification are beneficial to the control of distortion in quenched components, although the most desirable compositions are those that produce a lower rather than a higher M_s temperature.

MST/367     

Plane strain stress intensity factors for branched cracks

A method of calculating stress intensity factors for branched and bent cracks embedded in an infinite body has been developed. The branches are always assumed to be sharp cracks and are modelled by dislocation distributions. The original crack may be either sharp or of elliptical cross-section with finite root radius. Hence, the method which has a precision ±2%, is also applicable to the study of crack branches emanating from elliptical holes and, approximately, also from notches. The following detailed calculations have been made assuming mode I loading: branched sharp crack with branches of equal and different length, bent sharp crack, and one and two crack branches emanating from the crack with a finite root radius. Bending of a sharp crack under mixed mode loading has also been studied. The criteria of maximum tensile stress and maximum energy release rate used in the study of direction of crack propagation are discussed.     

Disbond effect on the stress intensity factor for repairing cracks with bonded composite patch

It is well known that the stress intensity factor is considerably reduced by the bonded composite repair. The finite element method is used to compute the stress intensity factor for repairing cracks with bonded composite patch taking account of the disbond. In the case of a disbond, the increase of patch thickness reduce the negative effects of disbond. The curves plotted show the concordance with the model [Thermal residual stresses in composite repairs on cracked metal structures, Ph.D. Thesis, University of British Columbia, 1998].     

Effect of transformation plasticity on generation of thermal stress and strain in quenched steel plates

Abstract

A viscoelastic–plastic mathematical model of the generation of thermal stress and strain in quenched steel plates has been extended to include the effect of stress on the characteristics of the martensite transformation. Stress dilatometry data are included for both the compressive and tensile cases and the results are introduced into the mathematical model either by using the concept of a reduction in yield stress or by use of an additional transformation strain. The use of either method produced an improved correlation between the calculated and experimentally determined residual stress and strain obtained after an oil quench, but this was at the expense of a reduced level of agreement in the case of water quenched material.

MST/12     

Analytical thermal stress model for a typical flip-chip (FC) package design

A simple analytical thermal stress model is suggested for a typical flip-chip (FC) lidded package design. The model is based on the concept of the interfacial compliance. The addressed design consists of a silicon FC bonded to an organic substrate and covered by a lid. The lid is configured in such a way that its mid-portion is bonded to the back side of the chip using a thermal interface material (a heat sink is intended to be subsequently mounted on the outer surface of the lid) and the lid’s peripheral portions are adhesively bonded to the same substrate using compliant attachments around the lid’s perimeter. A copper lid and a (hypothetical) organic lid are considered to develop a general feeling of the possible stress relief that could be expected if an organic lid is employed. The in-plane compliances of all the attachments, including the effective compliance of the encapsulated solder joint interconnections, are taken into account. A numerical example shows how the model could be used in practical computations. It shows also that the application of an organic lid, although is less attractive from the standpoint of the thermal management of the design, might result in appreciably lower thermal stresses. This is true for both the normal stresses in the chip’s cross-sections and the maximum interfacial shearing stresses at the chip’s ends. The developed model can be employed in the analysis of a FC package design of the type in question. Future work should include FEA verifications, and the suggested analytical stress model can be of help when developing a FEA preprocessing simulation model.     

Effects of short cracks produced at blunted pre-crack tip on stress and strain distributions

The present work investigates problems: (1) How are the plastic strain and the stress (triaxiality) re-distributed after a short crack initiated, extended and blunted at the pre-crack tip? (2) How do the above changes put a crucial effect on the triggering of the cleavage fracture? Based on the previous observations of configuration changes and fracture surfaces of pre-crack tips, Finite element method (FEM) simulations of a short crack initiated, extended and blunted at a pre-crack tip and calculations of distributions of stress, strain and triaxiality are carried out for 3PB pre-cracked HSLA steel specimens tested at -130^°C. The results reveal that: as long as the fatigue pre-crack is only blunted, in its vicinity a region where the accumulated strain is sufficient to nucleate a crack, and a region where the stress (triaxiality) is sufficient to propagate a crack nucleus are separated by a distance. The nucleated crack cannot be propagated and the cleavage fracture cannot be triggered. While a short crack produced at the fully blunted fatigue pre-crack, the strain retains, the stress (triaxiality) is rebuilt. An initiated and significantly extended and then blunted short crack makes a tip configuration, which on one hand is much sharper than that of the fully blunted original pre-crack tip, on other hand is wide enough to spread its effects into the high stress covered region. This sharpened crack tip configuration re-builds a ‘sharper’ distribution of stress (triaxiality) and makes two regions metioned above closer. Finally the two regions overlap each other and a cleavage crack can be initiated and propagated at a distance ahead of the blunted fatigue pre-crack.     

Localised strain and stress in bonded concrete overlays subjected to differential shrinkage

Bonded concrete overlays are widely used for repair and strengthening of existing structures as well as for precast elements which receive an in-situ topping. The performance of such overlays relates mainly to their resistance to cracking and debonding. Associated failure mechanisms are a result largely of differential volume changes between substrate and overlay. The objective of this paper is to provide an analytical tool to facilitate the design of bonded overlays for crack-resistance when subjected to shrinkage restraint. Fundamental strain characteristics of composite members are identified and existing analytical models for the prediction of strains and stresses in bonded overlays are evaluated. Results from experimental work indicate that existing models, which are based on simple beam theory, are deficient in modelling overlay strains realistically. The degree of overlay restraint was found to depend far less on relative section dimensions of substrate and overlay than is commonly assumed. Based on fundamental aspects concerning strain characteristics of bonded overlays, an analytical prediction model is introduced, based on localised strain conditions at the interface.     

Effect of substrate thickness on interfacial adhesive strength and thermal residual stress of second-generation high-temperature superconducting tape using peel test modeling

Second-generation high-temperature superconducting (2G HTS) tape is used in magnets and cables because of its outstanding electromagnetic characteristics. However, with the development of winding technology, thinner tapes are required in the construction of magnets. The effect of using thinner substrates on the resulting mechanical and electrical properties of 2G HTS tapes must thus be urgently understood. The interfacial adhesive strength is an important index used to characterize the mechanical strength of 2G HTS tape. Previous experimental studies have shown that thermal stress is one of the major factors in the delamination of the component tape used for magnet winding or cable assembly. In this study, the effect of substrate thickness on the interfacial adhesive strength of 2G HTS tape was investigated using peel test modeling. The thermal residual stresses accumulated during tape synthesis and caused by altered temperature during tape preparation and application at 77 K were also considered. To address the geometrical, physical, and boundary nonlinear problem, the finite element method was used. The simulation results indicate that interfacial stress caused by thermal shrinkage may separate the tape near the superconductor layer at the outer edge; however, no significant effect was observed for the central part. When the thermal residual stress was considered, the peel strength was reduced by approximately 20%. The substrate thickness also played an important role in the magnitude of thermal residual stress, which resulted in an increase of the peel strength with decreasing substrate thickness.     

Effect of magnetic field, thermal cycling and bending strain on critical current density of multifilamentary Bi-2223/Ag tape and fabrication of a pancake coil

Multifilamentary HTSC tapes are important for their applications in various electrical devices. Powder-in-tube technique with improved optimized synthesis parameters is regarded as one of the most promising ways to prepare long-length multifilamentary Bi-2223/Ag tapes. Nevertheless, usefulness of such tapes depends on their electrical and mechanical properties. Critical current density of a Bi-2223/Ag tape with 37 filaments has been studied at 77 K with field, field orientation, thermal cycling and bending strain as parameters. Results have been discussed in light of various mechanisms and models. A small pancake coil has been fabricated out of the same tape and the test results presented.     

Numerical analysis of the stress intensity factors for repaired cracks from a notch with bonded composite semicircular patch

In this paper, we investigated the crack growth behaviour of cracked thin aluminium plate repaired with bonded composite patch. The finite element method is used to study the performance of the bonded composite reinforcement or repair for reducing the stress concentration at a semicircular lateral notch and repairing cracks emanating from this kind of notch. The effects of the adhesive properties and the patch size on the stress intensity factor variation at the crack tip in mode I were highlighted. The obtained results show that the stress concentration factor at the semicircular notch root and the stress intensity factor of a crack emanating from notch are reduced with the increase of the diameter and the number of the semicircular patch. The maximal reduction of stress intensity factor is about 42% and 54%, respectively, for single and double patch. However, the gain in the patch thickness increases with the increase of the crack length and it decreases when the patch thickness increases. The adhesive properties must be optimised in order to increase the performance of the patch repair or reinforcement.     

Stress-function variational method for stress analysis of bonded joints under mechanical and thermal loads

High interfacial stresses near the ends of adherends are responsible for debonding failure of bonded joints used extensively in structural engineering and microelectronics packaging. This paper proposes a stress-function variational method for determination of the interfacial stresses in a single-sided strap joint subjected to mechanical and thermal loads. During the process, two interfacial shear and normal (peeling) stress functions are introduced, and the planar stresses of adherends of the joints are expressed in terms of the stress functions according to the static equilibrium equations. Two coupled governing ordinary differential equations (ODEs) of the stress functions are obtained through minimizing the complementary strain energy of the joints and solved explicitly in terms of eigenfunctions. The stress field of the joints based on this method can satisfy all the traction boundary conditions (BCs), especially the shear-free condition near the adherend ends. Compared to results based on finite element method (FEM) and other analytic methods in the literature, the present variational method is capable of predicting highly accurate interfacial stresses. Dependencies of the interfacial stresses upon the adherend geometries, moduli and temperature are examined. Results gained in this study are applicable to scaling analysis of joint strength and examination of solutions given by other methods. The present formalism can be extended conveniently to mechanical and thermomechanical stress analysis of other bonded structures such as adhesively bonded joints, composite joints, and recently developed flexible electronics, among others.     

Distributed cracks and kinked cracks in bonded dissimilar half planes with an interface crack

This paper is concerned with the interactions between an interface crack and other arbitrarily distributed cracks in two bonded dissimilar half planes. Special emphasis is placed on the cracks kinked at a tip of the interface crack, which remain unsolved as far as the authors are concerned. For the present, we pay attention to the stress intensity factors at the tips of the kinks or the distributed cracks, and not to those at the tips of the interface crack. The analysis is based on continuous distributions of the body forces along the cracks, and their densities are determined with a new procedure in order to get highly accurate results. The present analysis for distributed line cracks applies to kinked cracks, branched cracks and those piercing the interface just by joining some of the line cracks. Numerical calculations are performed for various important problems, and the effects of geometric and mechanical parameters on the stress intensity factors are examined.     

Boundary element analysis of thermal stress intensity factors for interface griffith and cusp cracks

The thermal stress intensity factors for interface cracks of Griffith and symmetric lip cusp types under vertical uniform heat flow in a finite body are calculated by the boundary element method. The boundary conditions on the crack surfaces are insulated or fixed to constant temperature. The relationship between the stress intensity factors and the displacements on the nodal point of a crack-tip element is derived. The numerical values of the thermal stress intensity factors for an interface Griffith crack in an infinite body are compared with the previous solutions. The thermal stress intensity factors for a symmetric lip cusp interface crack in a finite body are calculated with respect to various effective crack lengths, configuration parameters, material property ratios and the thermal boundary conditions on the crack surfaces. Under the same outer boundary conditions, there are no appreciable differences in the distribution of thermal stress intensity factors with respect to each material property. However, the effect of crack surface thermal boundary conditions on the thermal stress intensity factors is considerable.     

Mechanical model for the interfacial thermal stress in porous ceramic foam coatings bonded to a substrate

Abstract

Coatings of porous ceramic foams have potential applications in thermal protection systems of space shuttles. This paper develops a mechanics model for evaluation of thermal stress of porous ceramic foam coating/substrate structures under thermal shock temperature variation. Numerical results show that interfacial stresses exhibit singularity at the edge of ceramic foam coating. Stress intensity factor will reduce when ceramic foam coating has a larger density or a larger thermal conductivity. Comparison between beam model and membrane model is made and it suggests that consideration of bending stiffness is essential for correct evaluation of the thermal stress in the ceramic foams.