<p>In this licentiate thesis the work done in the project KME410 will be presented. The overall objective of this project is to evaluate and develop tools for designing against fatigue in single-crystal nickel-base superalloys in gas turbines. Experiments have been done on single-crystal nickel-base superalloy specimens in order to investigate the mechanical behaviour of the material. The constitutive behaviour has been modelled and verified by simulations of the experiments. Furthermore, the  microstructural degradation during long-time ageing has been investigated with  respect to the component’s yield limit. The effect has been included in the  constitutive model by lowering the resulting yield limit. Finally, the fatigue crack  initiation of a component has been analysed and modelled by using a critical plane approach.</p><p>This thesis is divided into three parts. In the first part the theoretical framework, based upon continuum mechanics, crystal plasticity and the critical plane approach, is derived. This framework is then used in the second part, which consists of three included papers. Finally, in the third part, details are presented of the used  numerical procedures.</p>

In this licentiate thesis the work done in the project KME410 will be presented. The overall objective of this project is to evaluate and develop tools for designing against fatigue in single-crystal nickel-base superalloys in gas turbines. Experiments have been done on single-crystal nickel-base superalloy specimens in order to investigate the mechanical behaviour of the material. The constitutive behaviour has been modelled and verified by simulations of the experiments. Furthermore, the  microstructural degradation during long-time ageing has been investigated with  respect to the component’s yield limit. The effect has been included in the  constitutive model by lowering the resulting yield limit. Finally, the fatigue crack  initiation of a component has been analysed and modelled by using a critical plane approach. This thesis is divided into three parts. In the first part the theoretical framework, based upon continuum mechanics, crystal plasticity and the critical plane approach, is derived. This framework is then used in the second part, which consists of three included papers. Finally, in the third part, details are presented of the used  numerical procedures.

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In this paper the mechanical behaviour, both elastic and plastic, of single-crystal nickel-based superalloys has been investigated. A theoretic base has been established in crystal plasticity, with concern taken to the shearing rate on the slip systems. A model of the mechanical behaviour has been implemented, by using FORTRAN, as a user defined material model in three major FEM-programmes. To evaluate the model a simulated pole figure has been compared to an experimental one. These pole figures match each other very well. Yielding a realistic behaviour of the model.

The increasing use of alpha/beta Ti-Al alloys in critical aircraft gas turbine engine and airframe applications necessitates the further development of physically-based constitutive models that account for their complex microdeformation mechanisms. Alpha/beta Ti-Al alloys are dual-phase in nature consisting of a mixture of hcp (alpha) and bcc (beta) crystal structures, which through variation in alloying elements and/or processing techniques can be produced in a wide range of microstructural compositions and morphologies. A constitutive model for these materials should address the various sources of material anisotropy and heterogeneity at both the micro and macroscales. The main sources of anisotropy in these materials are the low symmetry of the hcp phase, the texture, the relative strengths of different slip systems, non-planar dislocation core structures, phase distributions, and dislocation substructure evolution. The focus of this work is the development of a 3-D crystal plasticity model for duplex Ti-6Al-4V (Ti-64), an (alpha+beta) alloy. The model is used to study the process of attachment fatigue. Attachment fatigue is a boundary layer phenomenon in which most of the plastic deformation and damage accumulation occurs at depths on the order of tens of microns and encompasses regions of only a few grains into the depth of the material. The use of computational micromechanics-based crystal plasticity models to study attachment fatigue is a relatively new approach. This approach has the potential to offer additional insight to classical homogeneous plasticity models, since the length scales over which relative slip and crack initiation occur during this process is on the order of microstructural dimensions. Emphasis is placed on understanding the effects that texture, slip strength anisotropy, and phase distribution have on the surface and subsurface deformation fields during attachment fatigue. The deformation fields are quantified in terms of cumulative effective plastic strain distributions, plastic strain maps, and plastic strain-based critical plane multiaxial fatigue parameters.

Gamma-TiAl is an ordered intermetallic compound characterized by high strength to density ratio, good oxidation resistance, and good creep properties at elevated temperatures. However, it is intrinsically brittle at room temperature. This thesis investigates the potential for the use of grinding to process TiAl into useful shapes. Grinding is far from completely understood, and many aspects of the individual mechanical interactions of the abrasive grit with the material and their effect on surface integrity are unknown. The development of new synthetic diamond superabrasives in which shape and size can be controlled raises the question of the influence of those variables on the surface integrity. The goal of this work is to better understand the fundamentals of the abrasive grit/material interaction in grinding operations. Experimental, analytical, and numerical work was done to characterize and predict the resultant deformation and surface integrity on ground lamellar gamma-TiAl. Grinding tests were carried out, by analyzing the effects of grit size and shape, workpiece speed, wheel depth of cut, and wear on the subsurface plastic deformation depth (PDD). A practical method to assess the PDD is introduced based on the measurement of the lateral material flow by 3D non-contact surface profilometry. This method combines the quantitative capabilities of the microhardness measurement with the sensitivity of Nomarski microscopy. The scope and limitations of this technique are analyzed. Mechanical properties were obtained by quasi-static and split Hopkinson bar compression tests. Residual stress plots were obtained by x-ray, and surface roughness and cracking were evaluated. The abrasive grit/material interaction was accounted by modeling the force per abrasive grit for different grinding conditions, and studying its correlation to the PDD. Numerical models of this interaction were used to analyze boundary conditions, and abrasive size effects on the PDD. An explicit 2D triple planar slip crystal plasticity model of single point scratching was used to analyze the effects of lamellae orientation, material anisotropy, and grain boundaries on the deformation.

The use of metallic material systems (e.g. pure metals, alloys, metal matrix composites) in a wide range of engineering applications from medical devices to electronic components to automobiles continues to motivate the development of improved constitutive models to meet increased performance demands while minimizing cost. Emerging technologies often incorporate materials in which the dominant microstructural features have characteristic dimensions reaching into the submicron and nanometer regime. Metals comprised of such fine microstructures often exhibit unique and size-dependent mechanical response, and classical approaches to constitutive model development at engineering (continuum) scales, being local in nature, are inadequate for describing such behavior. Therefore, traditional modeling frameworks must be augmented or reformulated to account for such phenomena. Crystal plasticity constitutive models have proven quite capable of capturing first-order microstructural effects such as grain orientation, grain morphology, phase distribution, etc. on the deformation behavior of both single and polycrystals, yet suffer from the same limitations as other local continuum theories with regard to modeling scale-dependent mechanical response. This research is focused on the development, numerical implementation, and application of a novel, physics-based generalized (nonlocal) theory of single crystal plasticity. Two distinct versions of a dislocation-based micropolar single crystal plasticity theory are developed and discussed within the context of more prominent nonlocal crystal plasticity theories. The constitutive models have been implemented in the commercial finite element code Abaqus, and the size-dependent deformation of both single and polycrystalline metals have been studied via direct numerical simulation. A comparison of results obtained from the solution of several equivalent initial-boundary value problems using the developed models and a model of discrete dislocation dynamics has demonstrated the predictive capabilities of the micropolar theory and also highlighted areas for potential model refinement.

<p>In this paper the mechanical behaviour, both elastic and plastic, of single-crystal nickel-based superalloys has been investigated. A theoretic base has been established in crystal plasticity, with concern taken to the shearing rate on the slip systems. A model of the mechanical behaviour has been implemented, by using FORTRAN, as a user defined material model in three major FEM-programmes. To evaluate the model a simulated pole figure has been compared to an experimental one. These pole figures match each other very well. Yielding a realistic behaviour of the model.</p>

The demands for high density, fine pitch interconnections in electronics systems has seen solder-based approaches for such interconnections miniaturized to the scale of tens of micro meters. At such a small scale, such 'micro joints' may contain only one or a few grains and the resultant mechanical behaviour may not be that for a polycrystalline aggregate, but rather for a single crystal. Since the ~-Sn matrix of SnAgCu solder has a contracted body-centred tetragonal (BCT) structure, such a solder grain is expected to demonstrate a considerably anisotropic behaviour. In such cases the reliability of a Phfree solder is strongly dependent on the local microstructural features, such as the size and orientation of the grains. This thesis presents the investigation of the evolution of microstructure within a joint or at the interface and, the influence of such microstructural features on the meso-scale mechanical behaviour of the Ph-free solder. It includes Evolution of the interface between a molten solder and the Cu substrate To form a joint, the solder alloy is heated and molten, wetting a solid under-bump metallization. After solidification, layers of brittle intermetallic compounds (IMCs) are formed at the interface. In this project, facilities were set up to obtain interfacial reactants at an arbitrary moment of the liquid/solid reaction. Formation and evolution ~ during reflow of SnCu IMCs at the interface between the molten SnAgCu alloy and the Cu UBM was captured and presented for the first time. Formation of phases and IMCs with the body of a liquid SnAgCu solder during solidification The formation behaviour of basic components for a SnAgCu grain (including Sn dendrites, AIDSn and Cu6Sns IMCs) during solidification was investigated. Relationships between the growth behaviour of these components and their internal lattice orientation were studied. The characteristic growth and coupling of AIDSn IMCs and the Sn matrix to form eutectics has been elaborated and presented in this study for - 1- the first time. Based on the results, the forming process of a eutectic SnAgCu grain under the non-equilibrioum solidification condition was illustrated; and major factors that determine the lattice-orientation, size and substructure of the grain were discussed. Meso- and Micro- scale mechanical behaviour of a SnAgCu solder joint To study the size effect on the microstructure, and subsequently, the meso-scale mechanical behaviour, solder joints were manufactured with varying geometries. Shearing tests were performed on these meso-scale joints. The results first demonstrated that the anisotropic characteristics of a SnAgCu grain play an important role in the mechanical behaviour of both a meso-scale solder joint and the adjacent interfacial IMCs. To further investigate the micro-scale deformation and damage mechanisms, micro-mechanical tests were preformed within a SnAgCu grain. Constitutive equations for a SnAgCu grain Based on the experimental results, a crystal model was established to describe the local microstructure-dependent mechanical behaviour. The constitutive equation was implemented by means of the finite element approach, and applied in solder joints of a Flip Chip (FC) package by a multi-scale method. To describe the crystal behaviour at the higher temperature, the model was improved to account for deformations due to vacancy diffusion and thermal expansion. This model was integrated by an implicit approach, and implemented in a full three dimension (3D) finite element (FE) model.

Inhomogeneous deformation fields arising from the grain-grain interactions in polycrystalline materials have been evaluated using a crystal plasticity finite element method and extensively compared to neutron diffraction measurements under fatigue crack growth conditions. The roles of intergranular deformation anisotropy, grain boundary damage, and non-common deformation mechanisms (such as twinning for hexagonal close packed crystals) are systematically evaluated. The lattice misorientation field can be used to determine the intragranular deformation behavior in polycrystals or to describe the deformation inhomogeneity due to dislocation plasticity in single crystals. The study of indentation-induced lattice misorientation fields in single crystals sheds lights on the understanding of the scale-dependent plasticity mechanisms. A two-scale micromechanical analysis is performed to study the lattice strain distributions near a fatigue crack tip. The experimental finding of vanishing residual intergranular strain in polycrystals as the increase of the fully reversed loading cycles suggests the intergranular damage be the dominant failure mechanism. Our model predictions are compared to in situ neutron diffraction measurements of Ni-based superalloys under fatigue crack growth conditions. Predicted and measured lattice strains in the vicinity of fatigue crack tips illustrate the important roles played by the intergranular damage and the surrounding plasticity in fatigue growth. Motivated by the synchrotron x-ray measurements of lattice rotation fields in single crystals under indentation, the effect of the orientation of slip systems on the 2D wedge indentation of a model single crystal is investigated. Furthermore, the crystallographic orientations of the indented solids are gradually rotated, resulting changes of lattice misorientation patterns under the indenter. These 2D simulations, as well as a 3D Berkovich indentation simulation, suggest a kinematic relationship between the lattice misorientation and crystalline slip fields. Advanced structural materials such as light-weighted materials, nanocrystalline metals/alloys, and hierarchically structured alloys often encounter unconventional deformation mechanisms. The convolution of crystalline slip and deformation twin are considered in the hexagonal close packed polycrystals. Specifically, we have determined the lattice strain distributions near fatigue crack tips in Zircaloy-4, and the role of tensile-twins on intergranular strain evolution in a wrought Mg alloy, which compare favorable to available neutron diffraction measurements.