Wolfgang Mueller

Technische Universität Berlin | TUB · Institute of Mechanics

In den vorherigen Kapiteln haben wir bereits einige wichtige Grundbegriffe der Tensorrechnung kennengelernt, nämlich den Begriff der Metrik und den der ko- / kontravarianten Koordinatendarstellung inklusive ihrer anschaulichen Interpretation als Parallel-, respektive Orthogonalprojektion auf die Koordinatenachsen. Im nächsten Kapitel werden wir uns...

In Kapitel 3 wurde bereits darauf hingewiesen, dass die Grundaufgabe der thermo-mechanischen Kontinuumstheorie, nämlich die Bestimmung der fünf Felder der Massendichte, der Geschwindigkeit und der Temperatur zu allen Zeiten und in allen Punkten eines Körpers, neben Bilanzgleichungen auch Materialgleichungen erfordert. In der Tat werden aus den Bil...

Wir kommen nun auf unser Ausgangsproblem zurück, nämlich die in Kapitel 3 vorgestellten Bilanzen für die Masse, den Impuls und die Energie auf beliebige Koordinatensysteme umzuschreiben. Wir starten mit den Bilanzen in regulären Punkten und hier speziell mit der einfachsten Bilanz, nämlich der Massenbilanz, bei der es sich um eine skalare Gleichung...

Die Entropie und der zweite Hauptsatz der Thermodynamik gehören zu den physikalisch-technischen Konzepten, über die gerne viel Mystisches geschrieben wird. Das liegt wohl einerseits daran, dass die Entropie und die ihr zugeordnete Entropieproduktion relativ schwer fassbare, da abstrakte Größen sind, für die wir kein Bauchgefühl haben, anders als be...

In modern microelectronic systems solder materials are frequently used. Consequently, it is of great importance to predict their lifetime and stability. In order to perform such an analysis, material properties are required. Since electronic devices and therefore the amounts of used materials become smaller and smaller, the influence of a changing...

Das Buch führt in verschiedene Bereiche der Kontinuumstheorie ein, die für Ingenieure von Relevanz sind. Dazu gehören die Deformation des elastischen und des plastifizierenden Festkörpers, die Strömung reibungsfreier und reibungsbehafteter Fluide sowie die Elektrodynamik. Der Autor baut die Theorie im Sinne der Rationalen Mechanik auf, d.h. er unte...

Bekanntlich verwendet man in der Materialwissenschaft „Prinzipe“, um die mögliche Form von Materialgleichungen einzuschränken. Insbesondere sind hier das Entropieprinzip (etwa in der Version der Thermodynamik irreversibler Prozesse (TIP) nach [1], der Clausius-Duhem Formalismus nach [2] oder die Methode der Lagrange-Multiplikatoren [3]) zu nennen....

Hot-stage nanoindentation experiments were performed to analyze the temperature dependence of Young's modulus for two eutectic lead-free solder materials, namely Sn91Zn9 and Sn42Bi58. First results show discrepancies between the measurement results and values published in several references, especially at higher working temperatures when the homolo...

Wire-bonding is and will stay one of the essential interconnection methods in electronic packaging. Physics-based modeling of interconnects between the wire material and the substrate metallization has been constantly advanced over the last five years. Due to the variety and complexity of the mechanisms occurring during bonding it is required to cl...

Neben mechanischen Beanspruchungen sind mikroelektronische Bauteile stets einer wechselnden thermischen Belastung ausgesetzt. Für die Gewährleistung zuverlässiger Fügeverbindungen ist daher die Kenntnis der materialspezifischen Kennwerte der Fügewerkstoffe in Abhängigkeit der Temperatur zwingend erforderlich. Die Nanoindentation erlaubt es aus eine...

This work presents some recent progresses in reliability assessment of electronic assemblies in automotive industry and shows how coupled numerical-experimental techniques can help us save time and reduce the cost of IC package qualification. In order to fulfill the continuous trends in miniaturization of the electronic devices together with the de...

Further miniaturization of electronic systems is approaching new limits due to the failure mechanism of electromigration. Electromigration results in a transport of material in solder joints subjected to high electric current densities. This decreases the system reliability and, therefore, assessing and quantifying this failure mechanism becomes ne...

In this paper, we discuss lifetime prediction for flip chips under temperature and vibration loading in terms of the failure mechanisms related to solder joint fatigue. Our approach does not need additional data from the experiment but can be used in the design stage. For lifetime prediction solder fatigue coefficients from the literature and resul...

Electronic malfunction caused by thermal stresses is one major problem in modern electronic industries. Therefore, the precise knowledge of the mechanical solder material properties as a function of temperature is required. Nanoindentation and its potential of recording load-displacement curves is a widely-used miniature test for the determination...

Higher pin count and reduced pitch along with increased wafer size set new demands to fine pitch wafer probe technology. Vertical buckling probe needles are one of the available concepts. The required elasticity for contacting the pad is achieved by buckling of the needles. The buckling mode guarantees a consistent contact pressure over a large ran...

Interface formation between 25-μm AlSi1 wire and flash-Au substrate metallization during a bonding time of 50ms has been investigated. Only a few milliseconds after the ultrasonic power is switched on, intermetallic phase growth starts, continuing until the end of the wire-bonding process. During the entire bonding time, the fraction of the interfa...

The fabrication of microelectronic and micromechanical devices leads to the use of only very small amounts of matter, which can behave quite differently than the corresponding bulk. Clearly, the materials will age and it is important to gather information on the (changing) material characteristics. In particular, Young's modulus, yield stress, and...

In this paper we discuss the lifetime prediction for Pb-free soldered flip chip components under combined temperature cycling (TC) and vibration loading in terms of the failure mechanisms related to solder joint fatigue. We show the results of several experiments including failure analysis and comparison of lifetime models. For this purpose finite...

The continuous effort of modern electronic industry is the miniaturization of microelectronic components. In order to guarantee the reliability of the joining process, the quantitative knowledge of the solder material properties is very important, especially the values of Young's modulus, Nanoindentation hardness and yield stress. However, small-si...

Further miniaturization of electronic systems is approaching new limits due to the failure mechanism of electromigration. Electromigration results in a transport of material in solder joints subjected to high electrical current densities. This decreases the system reliability and, therefore, it is necessary to assess and quantify this failure mecha...

Microelectronic components are subjected to a continuous miniaturization process. These efforts of a modern electronic industry require quantitative knowledge of the solder material properties in order to guarantee the reliability of the joining process. Of particular interest are the values of Young's modulus and hardness. Corresponding to the sma...

Due to the demand of the industry for an increase of the number of I/Os, while decreasing the die size, the bond pads had to shrink and design restrictions for the active structures underneath had to fall. This leads to new challenges for the electrical probing and the mechanical robustness of the under-pad structures. This paper presents analytica...

Electronic assemblies in field use are exposed to a wide range of environmental loads. The interaction of combined loads has to be considered in lifetime estimates of electronic packages. In this paper, we discuss lifetime prediction for lead-free soldered flip chips under vibration load in different temperature environments in terms of solder join...

In this paper we discuss the influence of solder joint geometry on the lifetime of a flip chip assembly. Geometry variations caused by variations of solder volume, pad configuration, and pad size on the printed circuit board (PCB) were taken into account. Typically these parameters vary due to technological fabrication tolerances. Consequently, the...

A numerical method for the analysis of stresses and plastic flow rates is presented for processes with axisymmet-ric plastic flow of metals. This technique is based on a representation of yield zones in a special formulation of the stresses related to Iljushin's deviatoric stress space. The basic differential equations describing axisymmet-ric plas...

A model of deformation of stochastic composites subjected to microdamage is developed for the case of orthotropic materials with microdamages accumulating in the fibers. The composite is treated as a matrix strengthened with elliptic fibers with orthotropic elastic properties. The fractured microvolumes are modeled by a system of randomly distribut...

Material parameters has to be determined with regard to the influence of the solder volume and the crystal orientation to understand the thermo-mechanical properties and therefore the reliability of small lead free solder joints in microelectronics. The influence of crystal orientation to the reliability is very important because a small solder joi...

The book provides a systematic introduction into the fundamental ideas of thermodynamics at a somewhat advanced level. And it exhibits many applications of the theory in the fields of engineering, physics, chemistry, physical chemistry, and materials science. The universal equations of balance are strictly separated from the constitutive equations...

Interfacial adhesion is of important concern for multilayered structures such as microelectronic packages. Environmental effects, i.e., high temperatures and moisture diffusion, change the mechanical properties of polymeric materials and, more importantly, degrade the adhesion between the polymeric adhesives and substrates. Delamination between the...

For a heuristically important and qualitatively correct treatment of thermodynamic processes one usually ignores shear stresses, heat conduction, and temperature and pressure gradients. We have discussed the working \(\dot{W}\) of such idealized - reversible -processes in Paragraph 1.5.6. The stress work -or internal work* - done in the time dt is...

Moisture content Unsaturated moist air is a mixture of air and water vapor. Both are considered as ideal gases. Indeed, we use the ideal gas laws for water vapor all the way down to the state of saturation, where condensation occurs. For a given temperature this occurs at the pressure p′= p(T) which may be read off from Table 2.4.

Formulation and exploitation Formulation Rudolf Julius Clausius (1822-1888) has drawn conclusions from the following experience Heat cannot pass by itself pass from a colder to a warmer body or, in a later version Heat cannot pass from a colder to a warmer body without compensation. These are two formulations of the Second Law of thermodynamics. We...

Characterization of mixtures We consider mixtures, or solutions, or alloys with v constituents, which are characterized by a Greek index. Thus pα is the partial pressure of constituent α, ρα its density, and uα or sα are the specific values of the internal energy and entropy, respectively. Pressure, density, internal energy density, and entropy den...

It was Denis Papin – the inventor of the pressure cooker, cf. Paragraph 2.4.8 – who first condensed vapor and lifted a weight by doing so. He used a brass tube of diameter 5 cm; some water at the bottom was evaporated and the vapor pushed a piston upward which was then fixed by a latch. Afterwards the tube was taken away from the fire, the vapor co...

Stoichiometry We denote the mass of a constituent α in a homogeneous mixture by mα . The corresponding mass balance reads \( {{{\rm d}m_\alpha} \over {{\rm d}t}} = \tau_{\alpha}V, \alpha = 1,2, \cdots, v, \) (9.1) where τα is the density of mass production of constituent α. It is clear that the sum of all the v values τα must be equal to zero, beca...

The need for constitutive equations We recall the objective of thermodynamics which is the determination of the five fields mass density ρ(xi , t), velocity wj (xi ,t), temperature T(xi , t). (2.1) For this purpose we need five equations and we choose the five equations of balance of mass, momentum, and (internal) energy \({{\partial\rho} \over {\p...

The systematic development of the thermodynamic theory and its applications begins in Chap. 1 of this book. Some of the applications concern ideal gases, notably air. Others concern nearly incompressible fluids, notably water. Therefore it is appropriate to have the equations for ideal gases and incompressible fluids available at the outset. There...

Mass density, velocity, and temperature During a process the mass density, the velocity, and the temperature of a fluid are, in general, not homogeneous in space, nor are they constant in time. Therefore mass density, velocity, and temperature are called time-dependent fields. Fluid mechanics proposes to calculate the fields of mass density ρ(xi ,t...

Mass and momentum of a gas or a fluid are easy to interpret in terms of atoms and molecules: They are simply the sums of the masses and momenta of the constituent molecules. Pressure and temperature may also convincingly be interpreted by molecular processes and properties, e.g. see Prologue 4. Energy is more subtle: It is true that the kinetic ene...

The heat conduction equation In a body at rest with constant mass density and momentum the equations of balance of mass and momentum are identically satisfied, if we neglect thermal expansion, and the energy balance (1.48) – without radiation – is reduced to the form \( \rho{{\partial{u}}\over{\partial{t}}}+{{\partial{q_i}}\over{\partial{x_i}}}=0....

Available free energy We investigate the equilibrium of a liquid droplet in its vapor, and – at the same time – we discuss the equilibrium conditions for a vapor bubble surrounded by liquid. Fig. 11.1 shows the systems to be considered and introduces some notation. Droplets and bubbles are considered as spherical, p is the pressure on the outside a...

Für die zuverlässige Herstellung und den Gebrauch immer kleiner werdender Geräte und Strukturen ist die Kenntnis der zugehörigen Werkstoffeigenschaften unerlässlich. Deren Ermittlung muss an Miniaturproben durchgeführt werden, da die gebräuchlichen, auf Standardproben beruhenden Verfahren keine verlässlichen Aussagen über das Materialverhalten im µ...

During fabrication of modem microelectronic components miscellaneous solder materials are used. In order to ensure high quality of the manufacturing process as well as optimal reliability of the component and, in particular, of the solder joints it is most important to know the properties of all the materials involved. Of special interest are Young...

The pad metallization of multilayers is often built up by layers of Cu/Sn or Cu/Ni/Au which will be wetted during the reflow process by the solder material. Normally the Au layer protects the Ni against oxidation and the nickel layer suppresses the diffusion of Cu into the Sn and vice versa to produce intermetallic components (IMCs). In this way a...

Material parameters that describe the mechanical behavior of small test volumes realistically are required if the thermo-mechanical properties of microelectronic or micromechanical components are to be determined. Today the smallest microelectronic solder joints consist of only a few crystals, some-times even just a single one, and/or intermetallic...

The objective of this paper is presenting two energy based failure criteria and applying them in reliability simulations of Complementary Metal Oxide Semiconductor (CMOS) structures. Of particular interest are the Back-End-Of-Line (BEOL) interconnect layers and their interfaces. It is an accepted fact that process-induced flaws due to a mismatch in...

In order to analyze the micro-morphology evolution in today's (lead-free) solders we present a theory of multi- component heterogeneous solid mixtures based on fundamental thermodynamic principles. We derive an extended diffusion equation, which allows to predict the diffusion-induced phase separation and coarsening process within solids under the...

Delamination between the copper leadframe and the epoxy molding compound of microelectronic devices is a common failure concern. Interfacial adhesion characterizes the resistance of an interface to initiation and growth of interfacial delamination. In general, interface strength is an important factor for the successful fulfillment of package requi...

The reliable behavior of solder joints is a well-known key issue for the microelectronic industry. From the technological point-of-view SMT solders guarantee the electrical and mechanical bonding on a printed circuit board. Recently, environmental tendencies turn the attention to lead-free materials, the properties of which still have to be studied...

In this paper we will discuss the impact of residual stresses on the reliability of microelectronic components and the materials used therein. The following issues will be particularly emphasized: First, the tendency toward delamination and subsequent cracking along interfaces, such as between silicon dies, organic substrates, glues, and underfill...

The local response of a 3D periodic structure subjected to a spatial average of strain is studied. The governing differential equations for small displacement, linear elasticity theory are solved iteratively in Fourier space. Periodic boundary conditions as well as prescribed averages of strain are satisfied exactly a priori due to the use of Fouri...

Experimental investigations show that the microstructure of solders changes over time. In order to estimate the reliability and the lifetime of microelectronic solder materials it is important to predict the rate of microstructural change. Starting with an experimentally based overview on nucleation, spinodal decomposition as well as subsequent pha...

This paper focuses on a finite element analysis of the state of stress and strain within an intermetallic layer at the interface of a lead-free solder joint. The magnitude and sign of the stresses and strains (tensile vs. compressive) is discussed as a function of various parameters, such as the thermo-mechanical properties of the materials constit...

This paper presents some results on residual stress measurements in PSZ ceramics that were obtained by using confocal Raman spectroscopy. Moreover an attempt is made to understand and to model these stress fields by using anisotropic linear elasticity in context with Discrete Fourier Transforms (DFT). (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinh...

Focus of this paper is the prediction of silicon fracture in microchips of electronic devices. The strength of silicon chips strongly depends on flaw distributions introduced by wafer manufacturing processes. Consequently strength data scatter and a probabilistic approach to failure is required. For this purpose Weibull theory will be used and comb...

A method based on Fourier series is presented, which allows to calculate the local stress–strain response of a three-dimensional periodic structure subjected to a spatial average of strain. The periodicity allows the reduction of the problem to that of a Representative Volume Element (RVE). The solution operator (which can easily be calculated in F...

We investigate the mechanical properties of intermetallic phases in microelectronic structures with the help of nanoindentation. Moreover, we shall try to answer the question as to whether nanoindentation can be used to quantify the growth of intermetallic phases, at least at the interface of a solder connection. Different specimens and treatments...

In order to guarantee reliability of semiconductor devices for automotive applications an optimized package design is required. Clearly the design must be based on the best choice of geometry, materials and manufacturing processes. It is well known that the various process steps involved during package manufacturing occur at relatively high tempera...

To date the numerical simulation of gas-assisted laser cutting has successfully evaded rigorous treatment, mainly due to the complexity of the process, and the intrinsic highly dynamic behaviour of the melt pool and the presence of a shield gas jet. Contrary to the usual approach of adjusting simulation aims to fit the constraints of available hard...

The microstructures of solders in microelectronic components, lead containing as well as lead free, change over time. This is first of all due to comparatively high homologous temperatures which occur during reflow as well as during operation of the component. Moreover, because of the intrinsic thermal mismatch between the various materials that co...

Fluorescence microprobe spectroscopy was used in [1] to determine in situ microstress fields that develop during fracture in a model ceramic/metal composite. In particular, experimental and theoretical procedures were described in order to relate the experimental peak-shift to the various stress components and combinations thereof. Based on suitabl...

The reliability of semiconductor devices in automotive environmental conditions requires optimized package design with respect to geometry, materials and manufacturing processes. Process steps at high temperatures can result in high package stresses at operating temperatures due to mismatch of thermal expansion coefficients of the package compound...

In this paper we present our results on how nanoindentation can serve for measurement of (local) mechanical properties in microelectronic materials and components. Special attention is paid to the properties of interface regions, i.e., the region of intermetallic bonds. Finally a finite element model is presented in order to simulate the full inden...

The stress-strain response of a periodic structure due to an applied eigenstrain field is investigated. The periodic structure allows reduction of the problem to a representative volume element (RVE) problem. A review of Fourier series as a particular method of solving the set of differential equations is given, and an example problem is studied. R...

Current numerical simulations of laser materials processing are usually based on a greatly simplified process model in order to allow for short computation times. This significantly decreases their flexibility and ability for simulation of the great variation of today's processes and, consequently, accounting for their subtle but important differen...

Die Bestimmung der Materialparameter des Lotwerkstoffmodells spielt eine wichtige Rolle für die Modellierung des Materialverhaltens. Dabei enthalten die Lotwerkstoffmodelle sowohl elastisch-plastische als auch viskoplastische Materialparameter. Die Identifikation der Modellparameter anhand der Versuchsergebnisse stellt eine inverse Problemstellung...

This paper concentrates on open problems regarding recently published work in the field of modeling micromorphological changes in lead-free solders using phase field theories of the Cahn-Hilliard type. Specific examples will be eutectic SnPb, SnAg, and AgCu. After a short review of the phenomenology all the relevant equations will be set up, which...

This paper addresses the convergence characteristics of an iterative solution scheme of the Neumann-type useful for obtaining homogenized mechanical material properties from a representative volume element. The analysis is based on Eshelbys idea of "equivalent inclusions" and, within the context of mechanical stress/strain analysis, allows modeling...

This paper starts with an outline of the potential of phase field theories of the Cahn-Hilliard type when applied to studies of micromorphological change in solids. Various examples are presented ranging from ceramics to metals. The focus will be on a discussion of the material parameters involved during the modeling and how these can be specified...

A theoretical analysis is carried out in closed-form to quantitatively describe the pressing of an individual surface asperity into its elastic bulk when subjected to normal loads. To this end, a single asperity is simulated by a paraboloid of revolution of an arbitrary even power. The investigation is based on theory of elastic contact as original...

In recent years the study of heterogeneous bodies, i.e., the computation of local stress–strain fields which may arise due to elastic or thermal mismatches of the constituents or the computation of effective properties (homogenisation), based on the discrete Fourier transformation (DFT) becomes more and more attractive. In fact, several contributio...

We present in this paper a method for determining the convergence characteristics of the Neumann iterative solution of a discrete version of a second-type Fredholm equation. Implemented as the so-called 'equivalent inclusion problem' within the context of mechanical stress-strain analysis, it allows the modelling of elastically highly heterogeneous...

Continuous Fourier transforms (CFT) are used to derive analytical expressions for the stress and strain fields, respectively, in heterogeneous bodies consisting of cubic materials which additionally may be addressed to a uniform eigenstrain. The so-called “equivalent inclusion method” (Mura 1987) builds the starting point of this analytical method....

In this paper mechanical parameters of tin-lead and lead-free microelectronic solder materials will be determined. Specifically, the emphasis is on SnPb37 and SnAg3.8Cu0.7Bi2. The investigation is based on an experimental technique known as the small punch test (SPT) using different SPT displacement rates in combination with an appropriate numerica...

microstress fields that develop during fracture in an exemplary ceramic/metal composite. Stress maps are obtained over a relatively large area in the neighborhood of a propagating crack at both zero and critical loading conditions. Theoretical and experimental issues of concern for measurement of local complex stress fields are dealt with. In parti...

A strengthening mechanism merely arising from internal (residual) microstresses due to thermal expansion mismatch is proposed for explaining the high experimental strength data measured in Al2O3/SiC nanocomposites. Upon cooling, transgranular SiC particles undergo lower shrinkage as compared to the surrounding matrix and provide a hydrostatic “expa...

An approximate analytical 2-D solution for the strain field components 11, 12 and 22 occurring in a cubic material due to a coherently bonded shear eigenstrained inclusion of cylindrical geometry was obtained by means of Continous Fourier Transforms (CFT). A Discrete Fourier Transform (DFT) based numerical model was used in order to test the validi...

The temporal progress of phase separation and coarsening observed in eutectic tin/lead (SnPb) solders was investigated using computer modeling. The modeling framework is based on an extended diffusion equation of the phase-field model type that includes classical Fickean diffusion, effects of surface tensions according to the Cahn–Hilliard formalis...

The intent of this paper is to apply the technique of discrete Fourier transforms (DFT) to the computation of the stress and strain fields around holes in an externally loaded two-dimensional representative volume element (RVE). This is done to show that DFT is capable to handle geometries with rather sharp corners as well as steep gradients in mat...

This paper presents a quantitative simulation of the phase separation and coarsening phenomenon in eutectic tin/lead (SnPb) solders. The computer modeling is based on continuum theory and phase field models that were evaluated using the most recently available data for the free energy of the tin/lead system, diffusional and mobility coefficients, e...

The objective of our contribution is to present the discrete Fouriertransformation (DFT) as a serious alternative for the numerical computation of local stresses and strains in a two dimensional Representative Volume Element (RVE) containing heterogeneities of complex shape and high volume fractions. The methodology is based on the application of t...

This paper presents a model, which is capable to simulate the coarsening process observed during thermo-mechanical treatment of binary tin–lead solders. Fourier transforms and spectral theory are used for the numerical treatment of the thermo-elastic as well as of the diffusion problem encountered during phase separation in these alloys. More speci...

The objective of this paper is to investigate if and how transformation factors for the lifetime of modern, geometrically complex microelectronic components can be defined and obtained. Three types of components are investigated: BGAs, CSPs, and flip chips (FCs). The lifetime of each is based on the prediction of lifetime for their solder bumps. Th...

This paper presents lifetime predictions, based on finite element analysis (FEA), for the copper via connectors present in high density interconnectors (HDI) used for mounting of CSPs. The life-saving impact of various fillings of these connectors is investigated using different FE-sub-models for capture of the intricate HDI substructure. A ranking...

This paper presents a quantitative computer simulation of the coarsening phenomenon observed in eutectic tin/lead and other solder materials used for joining microelectronic components. The mathematical model is based on phase field theory and allows predicting the development of tin concentration over time within a representative volume element (R...

In order to model the aging of SMT (Surface Mount Technology) solder materials, which is a prerequisite for lifetime predictions of microelectronic joints as well as of the microelectronic package as a whole, it is necessary to know the current mechanical parameters of the solder as accurately as possible. In fact, the material behavior of solders...

This paper investigates whether and how discrete Fourier transforms (DFT) can be used to compute the local stress/strain distribution around holes in externally loaded two-dimensional representative volume elements (RVEs). To this end, the properties of DFT are first reviewed and then applied to the solution of linear elastic and time-dependent ela...

Continuous and discrete Fourier transforms (CFT and DFT, respectively) are used to derive a formal solution for the Fourier transforms of stresses and strains that develop in elastically homogeneous but arbitrarily eigenstrained linear-elastic bodies. The solution is then specialized to the case of a dilatorically eigenstrained cylindrical region i...

Complex stress potentials are derived to obtain an analytical solution for the stresses in epicycloidal specimens which contain a dislocation. The solution is used to obtain an analytical expression for the stress intensity factors of cusp-like cracks in such specimens which can be considered as a generalization of the well established concept of G...

The fatigue and damage of solder joints and the potential for interface failure within chip scale packages (CSP) are primarily caused by thermal loading. The thermally induced residual stresses depend on the thermal mismatch encountered during thermal cycle tests (TCT) and, for power cycle tests (PCT), on the gradient of the temperature distributio...

A general solution for the total strains that develop in elastically homogeneous and arbitrarily eigenstrained linear-elastic bodies is derived by means of continuous Fourier transforms (CFT). The solution is specialized to the case of a dilatorically eigenstrained spherical region in an infinite body, both of which are made of the same cubic mater...

The technique of complex potentials is used to derive an analytical solution for the stresses that develop in epicycloidal specimens subjected to hot spot loading. The solution gives stress intensity factors for cusp-like cracks in such specimens which can be considered as a generalization of the traditional Griffith crack. It is shown that by suit...

The J-integral technique is used to assess the risk of defects in a particular structure by explicit computation of the arising generalized forces. Three different situations are considered: stress concentrators in cycloidal specimens, the interaction of a dislocation with a circular inclusion, and the interaction between two dislocations. Special...