Prediction of crack initiation and propagation of adhesive lap joints using an energy failure criterion

In a previous paper, the present authors have pointed out limitations of some fracture mechanics parameters and shown that the vectorial J-integral can be applied to adhesive joints. Here, problems concerning the practical application of the vectorial J-integral are discussed and a more suitable failure criterion has been proposed, based on a specific strain energy criterion. The specific energy is not so sensitive to the size of the integration zone since it is ‘averaged’ over the volume of the zone. This criterion has been used to model the crack initiation and propagation in single lap joints with a brittle adhesive and a ductile adhesive. The effect of the shrinkage thermal stresses, adhesive fillet, surface preparation and type of adherends (aluminium and steel) were studied. The predicted failure loads and crack patterns are in very good agreement with the experimental results. One of the major conclusions is that the predictions can explain well the experimental scatter band that is always present in single lap joints due to the difficulty of controlling the adhesive fillet.     

THE USE OF A FAILURE ASSESSMENT DIAGRAM FOR INITIATION AND PROPAGATION OF DEFECTS AT HIGH TEMPERATURES

The use of a failure assessment diagram, of the type in the R 6 defect assessment procedure, is investigated for creep crack growth under steady loading. While a detailed approach based on C* remains attractive for appreciable creep crack growth, it is shown that a simplified approach can be formulated for limited crack extension. A failure assessment diagram is derived based on the option 2 curve of R 6 using isochronous stress-strain data. The inclusion of elastic strains in the isochronous data covers stress redistribution effects. Equations are given which enable a toughness, K_mat, for assessments at temperatures in the creep range to be evaluated from creep crack incubation and growth data presented in terms of C*. The toughness, K_mat, replaces the fracture toughness used in low temperature R 6 assessments. Thermal stresses can be included in assessments by evaluating the stress intensity factor for the combined thermal and mechanical loading. A formula is given which enables the effect of thermal stresses to be reduced when creep strains are sufficient to relax out part or all of the thermal stress.     

Fracture analysis of a steel sandwich with hardened core

2-D elasticity was employed to solve a thermal stress problem of a three layer laminated beam, in which each layer has different thermal expansion coefficient. The thermal stresses arise as a result that initially the layers of the beam were bonded at some high temperature T _Hsch and then quenched to some low temperature T _l . Elastic stress field can be derived and expressed in closed form by following the algorithm presented. A numerical example is presented to show that stress concentration due to this thermal effect at the ends of a laminated beam is high and steep enough to cause failure in an ultra-high carbon content and hardened steel.     

Thermal fatigue resistance characterization and ranking of materials using the V‐shape specimen testing method

Thermal fatigue resistance of materials is an extremely important criterion for the long‐term durability and reliability performance of very high‐temperature components and systems, such as advanced auto engine and exhaust systems. There is a broad range of material choices for thermal fatigue resistance applications. The final selection of the materials depends on the balance of engineering performance of the materials and the cost. To optimize the thermal fatigue resistance and cost of those materials, a reliable testing procedure for material thermal fatigue characterization and a material evaluation/selection matrix must be established. In this paper, the V‐shape specimen testing method in evaluating thermal fatigue resistance performance is introduced first. The influence of several factors, such as the thickness of specimens, operating temperature and hold time, on the thermal fatigue resistance is experimentally investigated. Subsequently, the statistical and probabilistic characteristics of the thermal fatigue failure data are analysed to reveal the possible failure mechanisms. Finally, a general rational approach for thermal fatigue resistance characterization and ranking is demonstrated, and a simple parameter λ = kσ_f/Eα, which combines the material strength, thermal conductivity and thermal expansion, is found to be the new breakthrough parameter, correlating to V‐shape thermal fatigue test results. Results on four currently used stainless steels verify the correlations and indicate the validity of this approach.     

Evaluation of deformation properties of asphalt mixture using aggregate slip test

Asphalt mixture is a multiphase particulate material composed of aggregate, asphalt and filler. The deformation property of asphalt mixture is an external reflection of aggregate slip behaviour. To evaluate the high-temperature deformation properties of asphalt mixture, an aggregate slip device was developed and aggregate slip tests were conducted on five asphalt mixtures for different gradations under different test conditions. Four evaluation parameters, the slip failure load (F_s), the slip failure deformation (D_s), slip modulus parameter (M) and slip energy index (SEI), were obtained according to the load–displacement curves. The relationship between these parameters and rut depth (RD) was analysed. The effects of test temperature and asphalt content on slip resistance of asphalt mixture are studied in this research. The results indicate that the parameter F_s has limitations for large nominal maximum particle-size mixture, and SEI is an effective parameter to evaluate the aggregate slip properties for different nominal maximum particle-size asphalt mixtures. SEI has the strongest relationship to RD, which is the best parameter to evaluate the slip deformation behaviour of asphalt mixture. With the increase in asphalt content, SEI has a peak value and a valley value. When the optimum asphalt content is used in asphalt mixture, aggregate skeleton effect and asphalt cohesive force can both reach a high level, and asphalt mixture has the best deformation resistance.     

Thermal and thermally stressed state of annular specimens for thermomechanical fatigue tests on materials. Communication 2

A procedure and analytical calculation are described for the thermal state of annular specimens with parabolic end surfaces necessary in order to choose the geometric shape and test schedules which provide excitation of prescribed thermal stresses. Values of temperature, thermal and mechanical bending, and contact stresses are prescribed which provide a specific type of material failure taking account of features close to holes and wedge tapers. Since specimen shape has some properties of the simplest multidimensional bodies it is possible to calculate the thermal state analytically.This study has been financed as part of the project: The use of new high-temperature materials, including coated materials, for the purpose of increasing the economic efficiency of aviation and marine engines. (Topic 5.2.3 of the Ukrainian State Committee of Science and Technology.Translated from Problemy Prochnosti, No. 7, pp. 39–47, July, 1993.     

The influence of residual stresses on the mechanical and thermal properties of injection moulded ABS copolymer

The mechanical and thermal properties of acrylonitrile-butadiene-styrene copolymer (ABS) were determined for as-moulded and annealed specimens in order to assess the influence of residual stresses on these properties. Mouldings were heat treated at temperatures below and above the glass transition temperature, T _g. Annealing below the glass transition removes most of the residual stresses arising during the moulding process, while annealing above the glass transition temperature removes both the residual stresses and molecular orientation. Residual stresses have a strong bearing on the end-use properties. The thermal behaviour of the mouldings are mostly affected by the stimulation of molecular motion caused by the relaxation of the residual stresses near the glass transition temperature.     

Effect of thermomechanical loads on the propagation of crack near the interface brittle/ductile

The purpose of this paper is to understand the combined effect of thermal and mechanical loading on the initiation and behaviour of sub-interface crack in the ceramic. In this study a 2D finite element model has been used to simulated mixed mode crack propagation near the bimaterial interface. The assembly ceramometalic is subjected simultaneously to thermomechanical stress field. The extent of a plastic zone deformation in the vicinity of the crack-tip has a significant influence on the rate of its propagation. The crack growth at the joint specimen under four-point bending (4PB) loading and the influence of residual stresses was also evaluated by the maximum tensile stress criterion. The J-integral at the crack tip is generally expressed by the thermomechanical local stresses. The results obtained show the effect of the temperature gradient ΔT, the size of the crack and the applied stresses on the J-integral.     

Research on Au-Al bonding properties based on a thermal shock environment

The thermal shock experiment of Au-Al bonding has been carried out. The mechanical characteristics, structure morphology and electrical characteristics degradation mechanism have also been researched. No cracks were observed in the bonding interface, and the bonding joints also showed good mechanical characteristics with pull stress of 3.0 to 12.0 g. Due to high temperature, the Au-Al intermetallic compound Au₅Al₂ with high resistibility was formed, which ultimately led to electrical failure. For the samples that were fabricated on the basis of the present technique, the bonding reliability has been evaluated. It has been found that the lifespan rule obeys the Weibull distribution, and at a high temperature of 150°C under 95% confidence level, the estimated results are η = 547 h, m = 3.83. In a room temperature environment, the Au-Al bonding samples’ lifespan has also been predicted on the basis of the rule of reliability evaluation. The result shows that the lifespan is about 20 years, while the reliability degree is 90%. Translated from Journal of Functional Materials, 2006, 37(10): 1,539–1,541, 1,544 (in Chinese)     

Strain energy release rate for interfacial cracks between dissimilar media

An analysis was made of the stresses along a bonded interface between two elastic half spaces of dissimilar isotropic materials. Various loading conditions which give rise to interfacial crack propagation were considered, including thermal loads, bending loads and tensile loads parallel to the bond. From this two-dimensional stress analysis, the strain energy release rate, _ct, was formulated as a fracture criterion for interfacial failure. Experimental studies conducted on specimens of epoxy bonded to aluminium demonstrated that this fracture criterion can be used to characterize debonding. It was also found that residual stresses contribute to the energy required for crack propagation and that increased local surface roughness resulted in increased fracture toughness.     

Thermal shock resistance of laminated ceramic matrix composites

The thermal shock resistance capability of laminated ceramic matrix composites is investigated through the study of three-dimensional transient thermal stresses and laminate failure mechanisms. A (–45°/45°)_s SiC/borosilicate glass laminate is utilized as a reference composite system to demonstrate the analytical results. The maximum allowable temperature change, T _max, has been taken as a measure of the thermal shock resistance capability of composites. The effects of fibre orientation, volume fraction, thermal expansion coefficient. Young's modulus, and thermal conductivity on the thermal shock resistance capability, expressed in terms of the maximum allowable temperature change, T _max, have been assessed. Numerical computations are also performed for six composite systems.     

Comparison of residual stresses in Ti–6Al–4V and Ti–6Al–2Sn–4Zr–2Mo linear friction welds

Abstract

In this paper, the levels of residual stress in the vicinity of linear friction welds in Ti–6Al–4V (Ti-64), a conventional α–β titanium alloy, and Ti–6Al–2Sn–4Zr–2Mo (Ti-6242), a near α titanium alloy with higher temperature capability, are mapped and contrasted. The alloys have significantly different high temperature properties and the aim of this work was to investigate how this might affect their propensity to accumulate weld residual stresses and their response to post-weld heat treatment. Measurements are reported using high energy synchrotron X-ray diffraction and the results are compared to those made destructively using the contour method. The strain free lattice plane d ₀ variation across the weld has been evaluated using the biaxial sin²Ψ technique with laboratory X-rays. It was found that failure to account for the d ₀ variation across the weld line would have led to large errors in the peak tensile stresses. Contour method measurements show fairly good correlation with the diffraction results, although the stresses are underestimated. Possible reasons for the discrepancy are discussed. The peak tensile residual stresses introduced by the welding process were found to be greater for Ti-6242 (～750 MPa) than for Ti-64 (～650 MPa). Consistent with the higher temperature capability of the alloy, higher temperature post-weld heat treatments have been found to be necessary to relieve the stresses in the near α titanium alloy compared to the α+β titanium alloy.     

Thermo-Mechanical Failure Criterion at the Micron Scale in Electronic Devices

Thermo-mechanical failures may occur in the passivation layer of micro-electronic devices during the fabrication process. These are in form of cracks which initiate at keyhole corners. In order to predict and eventually prevent these cracks a failure criterion is presented, based on an average value of the elastic strain energy in the vicinity of a reentrant corner of any angle. The proposed strain energy density (SED) failure criterion is validated by a test including 24 full size wafers which have been fabricated with different parameters: the interconnects (metal lines) height, the passivation thickness, and the passivating plasma power which was shown to correlate with the mechanical properties of the passivation layer. For each wafer, a FE model has been constructed, and the SED computed. It has been clearly shown, that above the critical value of SED _cr[R=0.15μm]≈1000 [J/m ³], all wafers manufactured were cracked. The SED criterion seems to correlate well with the empirical observations, and may be used as a standard tool for the mechanical design of failure free micro-electronic devices.     

Temperature effects on the fatigue of highly filled PMMA

The modulus and fracture toughness of an ATH-filled PMMA composite are determined as a function of temperature. The modulus can be modelled as a series addition of the two phases, giving a decreasing modulus with temperature tending to zero at 110°C. The K_1C value remains constant. Fatigue crack growth data in the form of da/dN versus K were obtained as a function of temperature and modelled using the Paris Law. The power index remained constant at 7.5, but the coefficient had a maximum at 50°C. It is suggested that this arises from microcracks generated by interparticle thermal stresses which are shown to have a maximum at the same temperature (50°C). A two-stage zone fatigue crack growth model was also applied to the data and gave a damage stress which correlated with the thermal stress and suggested a criterion based on achieving a constant energy per unit area.     

Thermal-Conductivity Characterization of Gas Diffusion Layer in Proton Exchange Membrane Fuel Cells and Electrolyzers Under Mechanical Loading

Accurate information on the temperature field and associated heat transfer rates is particularly important for proton exchange membrane fuel cells (PEMFC) and PEM electrolyzers. An important parameter in fuel cell and electrolyzer performance analysis is the effective thermal conductivity of the gas diffusion layer (GDL) which is a solid porous medium. Usually, this parameter is introduced in modeling and performance analysis without taking into account the dependence of the GDL thermal conductivity λ (in W · m⁻¹ · K⁻¹) on mechanical compression. Nevertheless, mechanical stresses arising in an operating system can change significantly the thermal conductivity and heat exchange. Metrology allowing the characterization of the GDL thermal conductivity as a function of the applied mechanical compression has been developed in this study using the transient hot-wire technique (THW). This method is the best for obtaining standard reference data in fluids, but it is rarely used for thermal-conductivity measurements in solids. The experiments provided with Quintech carbon cloth indicate a strong dependence (up to 300%) of the thermal conductivity λ on the applied mechanical load. The experiments have been provided in the pressure range 0 < p < 8 MPa which corresponds to stresses arising in fuel cells. All obtained experimental results have been fitted by the equation λ = 0.9log(12p + 17)(1 − 0.4e^−50p ) with 9% uncertainty. The obtained experimental dependence can be used for correct modeling of coupled thermo/electro-mechanical phenomena in fuel cells and electrolyzers. Special attention has been devoted to justification of the main hypotheses of the THW method and for estimation of the possible influence of the contact resistances. For this purpose, measurements with a different number of carbon cloth layers have been provided. The conducted experiments indicate the independence of the measured thermal conductivity on the number of GDL layers and, thus, justify the robustness of the developed method and apparatus for this type of application.     

Designing for ultrahigh-temperature applications: The mechanical and thermal properties of HfB2, HfC x , HfN x and αHf(N)

The thermal conductivity, thermal expansion, Young's Modulus, flexural strength, and brittle-plastic deformation transition temperature were determined for HfB₂, HfC_0.98, HfC_0.67, and HfN_0.92 ceramics. The mechanical behavior of Hf(N) solid solutions was also studied. The thermal conductivity of modified HfB₂ exceeded that of the other materials by a factor of 5 at room temperature and by a factor of 2.5 at 820°C. The transition temperature of HfC exhibited a strong stoichiometry dependence, decreasing from 2200°C for HfC_0.98 to 1100°C for HfC_0.67 ceramics. The transition temperature of HfB₂ was 1100°C. Pure HfB₂ was found to have a strength of 340 MPa in 4 point bending, that was constant from room temperature to 1600°C, while a HfB₂ + 10% HfC _x had a higher room temperature bend strength of 440 MPa, but that dropped to 200 MPa at 1600°C. The data generated by this effort was inputted into finite element models to predict material response in internally heated nozzle tests. The theoretical model required accurate material properties, realistic thermal boundary conditions, transient heat transfer analysis, and a good understanding of the displacement constraints. The results of the modeling suggest that HfB₂ should survive the high thermal stresses generated during the nozzle test primarily because of its superior thermal conductivity. The comparison the theoretical failure calculations to the observed response in actual test conditions show quite good agreement implying that the behavior of the design is well understood.     

The thermal shock of ß-alumina

The thermal shock of sodiumβ-alumina with relative densities from 60 to 98% theoretical has been investigated over the temperature range 150 to 700° C by quenching into water. The samples were ring segments cut from electrolyte tubes and were subsequently tested in both compression and tension. For relative densities of 75% and below the thermal shock damage was typical of stable crack growth and a steady decline in strength with sintering temperature was observed. For relative densities of 95% and above, thermal shock causes unstable crack growth and a critical value of ΔT was observed in the range 170 to 250° C depending on initial strength. From the linear relationship between observed ΔT _c and the thermal shock resistance parameter,R, it was concluded that the rapid heat transfer during quenching was nucleate water boiling and that cooling from ∼110° C to 0° C was not responsible for damage. The fracture stress after thermal shock above ΔT _c was consistent and showed little dependence on initial strength for relative densities ⩾95%. However, the fractional reduction in strength was related to the damage resistance parameterR‴. An estimate of the energy expended in fracture has been made, based on microscopic observation and compared with estimates of the stored strain energy due to thermal stresses.     

Adhesive features of bonded interfaces subjected to temperature shock

Abstract

Defects on interfaces can gradually degrade the interfacial adhesion of IC package layers. This can be attributed to an unmatched coefficient of thermal expansion in the materials subjected to the temperature change. This study employed a fuzzy controller to stabilize both delamination force and energy absorption in order to represent adhesion strength. The three controllable factors were: dwell time, solder mask thickness and shock temperature; and the two uncontrollable factors were: delamination force and energy absorption.

Temperature shock was used to simulate environmental temperature destruction, and delamination force was employed to simulate a shear test. Dropped destruction (energy absorption) was reproduced in an impact test. An analysis of variance (ANOVA) was conducted to determine significant factors, the optimal quality, and the most damaging conditions. Finally, the delamination force and energy absorption were combined using fuzzy logic in order to analyze the multiple performance characteristics index (MPCI). The MPCI is the only index of specimen quality levels that can determine the effects of temperature on the interfacial adhesion strength of a substrate/solder mask under certain conditions.     

Effect of modulus and cohesive energy on critical fibre length in fibre-reinforced composites

The effect of fibre modulus and cohesive energy on critical fibre length and radius in ceramic-fibre-reinforced brittle composites has been investigated employing both analytical theory and computer simulation. The theory consists of a shear-lag analysis in which an energy failure criterion is incorporated. The simulation consists of a two-dimensional computer model based upon a discrete network of grid points. Failure is also defined in terms of an energy criterion, where the energy is calculated on the basis of a two- and three-body interaction between the grid points. Both theory and simulation show that a minimum critical aspect ratio is found as a function of the elastic moduli ratio, E _f/E _m, with a divergence occurring at both low- and high-modulus values. As the modulus ratio is increased, there is a transition in failure mechanism from tensile-dominated failure in the matrix to shear-dominated failure at the fibre-matrix interface. In addition, families of critical aspect ratio curves are obtained as a function of the cohesive energy ratio, U _f/U _m. Larger cohesive energy ratios shift the critical aspect ratio curve to larger values. These features potentially explain trends in the experimental results reported by Asloun et al., where the critical fibre aspect ratio was measured for fibre/matrix systems having different modulus and toughness ratios.     

Reliability assessment and mechanical characterization of Cu and Au ball bonds in BGA package

Extended reliability and mechanical characterisation of Au and Pd-coated Cu (Cu) ball bonds are useful technical information for Au and Cu wire deployment in semiconductor device packaging. This paper discusses the influence of wire type on the package reliability and mechanical performance after several component reliability stress tests. Failure analysis has been conducted to identify the associated failure mechanisms of Au and Cu ball bonds after reliability tests. Wire pull strength and ball bond shear (with its break modes) of both wire types are investigated after unbiased highly accelerated temperature and humidity stress test (UHAST), temperature cycling (TC) and high temperature storage life test (HTSL) at various aging temperatures. Reliability Weibull plots have been plotted for each reliability stresses. Obviously Au ball bond is found with longer time-to-failure in Unbiased HAST stress compare to Cu ball bonds. Cu wire exhibits equivalent package and or better reliability margin compare to Au ball bonds in TC and HTSL tests. Failure mechanisms of UHAST and HTSL have been proposed and its mean-time-to failure (t₅₀), characteristics life (t_63.2, η) and shape parameter (ß) have been discussed in this paper.