Thomas R. Bieler

Superplasticity in powder metallurgy aluminum alloys and composites

Superplasticity in powder metallurgy aluminum alloys and composites has been reviewed through a detailed analysis. The stress-strain curves can be put into four categories: a classical well-behaved type, continuous strain hardening type, continuous strain softening type and a complex type. The origin of these different types of stress-strain curves is discussed. The microstructural features of the processed material and the role of strain have been reviewed. The role of increasing misorientation of low angle boundaries to high angle boundaries by lattice dislocation absorption is examined. Threshold stresses have been determined and analyzed. The parametric dependencies for superplastic flow in modified conventional aluminum alloys, mechanically alloyed alloys and aluminum alloy matrix composites is determined to elucidate the superplastic mechanism at high strain rates. The role of incipient melting has been analyzed. A stress exponent of 2, an activation energy equal to that for grain boundary diffusion and a grain size dependence of 2 generally describes superplastic flow in modified conventional aluminum alloys and mechanically alloyed alloys. The present results agree well with the predictions of grain boundary sliding models. This suggests that the mechanism of high strain rate superplasticity in the above-mentioned alloys is similar to conventional superplasticity. The shift of optimum superplastic strain rates to higher values is a consequence of microstructural refinement. The parametric dependencies for superplasticity in aluminum alloy matrix composites, however, is different. A true activation energy of 313 kJ mol−1 best describes the composites having SiC reinforcements. The role of shape of the reinforcement (particle or whisker) and processing history is addressed. The analysis suggests that the mechanism for superplasticity in composites is interface diffusion controlled grain boundary sliding.

Influence of Sn Grain Size and Orientation on the Thermomechanical Response and Reliability of Pb-free Solder Joints

The size and crystal orientation of Sn grains in Pb-free, near eutectic Sn-Ag-Cu solder joints were examined. A clear dependence of the thermomechanical fatigue response of these solder joints on Sn grain orientation was observed (Sn has a body centered tetragonal crystal structure). Fabricated joints tend to have three orientations in a cyclic twin relationship, but among the population of solder balls, this orientation triplet appears to be randomly oriented. In thermally cycled joints, solder balls with dominant Sn grains having the particular orientation with the c-axis nearly parallel to the plane of the substrate were observed to fail before neighboring balls with different orientations. This results from the fact that the coefficient of thermal expansion of Sn in the basal plane (along the alpha-axis) is half the value along the c-axis; joints observed to be damaged had the maximum coefficient of thermal expansion mismatch between solder and substrate at the joint interface, as well as a tensile stress modes during the hot part of the thermal cycle. Localized recrystallization was observed in regions of maximum strain caused by differential expansion conditions, and its connection with crack nucleation is discussed.

Flow softening during hot working of Ti-6Al-4V with a lamellar colony microstructure

The production of conventional alpha/beta titanium alloys for aerospace applications is often based on an ingot metallurgy approach comprising melting and a series of hot working and heat treatment steps. Recent research has probed the effect of factors such as prior-beta grain size, strain rate, and temperature on plastic flow and microstructure evolution during hot forging of Ti-6Al-4V with a lamellar colony microstructure. In particular, the flow softening response evident in true stress-strain curves determined from isothermal hot compression tests has been studied in an attempt to ascertain the important deformation mechanism. The objective of the present work was to determine if crystallographic texture changes, as characterized by nominally uniform rotation of the alpha phase, or platelet kinking within the lamellar colonies are major considerations that can explain the flow softening observations. This understanding is very important with regard to the eventual development of models for the prediction and control o texture and hence properties such as stiffness and fatigue resistance. To this end, the flow response during both isothermal, hot compression and hot tension testing was measured and interpreted with the aid of finite element and polycrystalline plasticity modeling.

Influence of Sn grain size and orientation on the thermomechanical response and reliability of Pb-free solder joints

The size and orientation of Sn grains in Pb-free, near eutectic SAC solder joints were examined. A clear dependence of the thermomechanical response of these solder joints on Sn grain orientation was observed. Solder balls with Sn grains of particular orientation (a-axis perpendicular to the substrate) were observed to fail before neighboring balls with different orientations. This results from the fact that the coefficient of thermal expansion of Sn along the a-axis is half the value along the c-axis; joints observed to be damaged had maximum mismatch in the coefficient of thermal expansion between solder and substrate at the joint interface, as well as tensile stress modes during the hot part of the cycle

Mechanism of high strain rate superplasticity in aluminium alloy composites

Abstract A constitutive equation has been obtained through an analysis of high strain rate superplasticity (HSRS) data on a 2124 Al Si 3 N 4 composite. The parametric dependencies of HSRS in composites are different from those observed in conventional aluminium alloys and mechanically alloyed alloys. The HSRS in composites exhibits high activation energy values of 293–338 kJ mol −1 and an inverse grain size and reinforcement size dependence. It is suggested that the mechanism of HSRS in composites is “interface controlled” superplasticity. This is depicted on a new “superplasticity mechanism map for composites”. The map can be used as a guideline for designing composites for optimum superplasticity.

An in-situ observation of mechanical twin nucleation and propagation in TiAl

Abstract A creep-deformed Ti-48at.% A1-2at.% Nb-2at.%Cr specimen was studied using the electron beam illumination method in a transmission electron microscope to investigate mechanical twin nucleation and propagation in situ. The mechanical twins were observed to nucleate by bowing out one or two twinning dislocations at grain boundaries. The mechanical twin nucleus was either an intrinsic stacking fault or an extrinsic stacking fault. The mechanical twin propagated by sequential emission of twinning dislocations from the grain boundaries and homogeneous glide of the twinning dislocations on every adjacent twinning plane. The twinning dislocation is identified to be 1/6[112] and the twinning plane is (111). The twin-matrix interface structure is also identified. A Schmid factor analysis indicates that the observed twin nucleation and propagation resulted from a local stress concentration. A simplified uniaxial tensile stress slate necessary to operate (111)[112] twinning system is analysed. Based on the e...

An automated method to determine the orientation of the high-temperature beta phase from measured EBSD data for the low-temperature alpha-phase in Ti–6Al–4V

A method was developed to determine the orientation of the high-temperature beta phase from measured electron-backscatter diffraction (EBSD) data for the low-temperature alpha phase in Ti-6Al-4V. This technique is an improvement over existing methods because it does not require a priori knowledge of the variant selection process and can accommodate variants from adjacent beta grains being incorporated in the data set submitted for analysis. It is a general method and therefore can be used to examine texture relationships in materials other than Ti-6Al-4V which undergo a burgers-type phase transformation.

Formation and growth of interfacial intermetallic layers in eutectic Sn-Ag solder and its composite solder joints

Single shear lap joints were made by soldering two Cu substrates with eutectic Sn-Ag solder, and its composite solders containing FeSn/FeSn2 or Ni3Sn2 intermetallic particles introduced by an in-situ method. Ageing of solder joints was performed at 70, 100, 120, 150, 180 °C for 1400 h. The growth of the interfacial intermetallic compound (IMC) layers was characterized assuming diffusion-controlled growth kinetics. Effects of such FeSn/FeSn2 and Ni3Sn4 particulates on the IMC layer growth rate were extensively characterized. Composite solder joints in the fabricated condition formed thinner IMC layers compared to the corresponding non-composite solder joints. The Cu6Sn5 IMC layer grew faster at temperatures above 120 °C (T/Tm=0.8), while growing slower at temperatures below 120 °C in composite solder joints. In-situ introduced FeSn/FeSn2 and Ni3Sn4 particle reinforcements in composite solder joints proved effective in reducing the overall growth of the interfacial Cu6Sn5 IMC layer only at lower temperatures. Composite solder joints exhibited slower growth of the Cu3Sn layer during ageing at all temperatures used in this study. Two different regions having different activation energies depending on the temperature were identified for the growth of Cu6Sn5 and Cu3Sn IMC layers.

The high strain rate superplastic deformation mechanisms of mechanically alloyed aluminum IN90211

Abstract The tensile behavior of mechanically alloyed (dispersion strengthened) IN90211 was investigated at strain rates between 0.0001 and 340 s−1 at temperatures between 425 and 475 °C. At strain rates above 0.1 s−1, superplastic elongations were obtained (maximum elongation of 525% at 475 °C and 2.5 s−1). Superplastic elongations were found to result from grain boundary sliding. The data were analyzed assuming that a threshold stress resists dislocation motion. The threshold stresses were obtained assuming n = 2 (grain boundary sliding) or n = 3 (solute drag) for the stress exponent. Both assumptions provided equally credible values for a temperature-dependent threshold stress between 1% and 20% of the Orowan looping stress. The n = 3 threshold stresses agreed with load relaxation data, but the n = 2 values corresponded to the lower limit of the superplastic deformation regime, as indicated by creep tests at lower strain rates. Based upon the threshold stress theories in the literature, the threshold stresses are suggested to arise from a combination of local and general climb of lattice dislocations over particles. Consideration of the activation energies, details of flow behavior, and stress relaxation experiments provided strong evidence for the n = 3 solute drag mechanism to be the rate-limiting process in the superplastic deformation regime.

Crystal Plasticity Finite Element Methods in Materials Science and Engineering

Preface INTRODUCTION TO CRYSTALLINE ANISOTROPY AND THE CRYSTAL PLASTICITY FINITE ELEMENT METHOD PART I: Fundamentals METALLURGICAL FUNDAMENTALS OF PLASTIC DEFORMATION Introduction Lattice Dislocations Deformation Martensite and Mechanical Twinning CONTINUUM MECHANICS Kinematics Mechanical Equilibrium Thermodynamics THE FINITE ELEMENT METHOD The Principle of Virtual Work Solution Procedure - Discretization Non-Linear FEM THE CRYSTAL PLASTICITY FINITE ELEMENT METHOD AS A MULTI-PHYSICS FRAMEWORK PART II: The Crystal Plasticity Finite Element Method CONSTITUTIVE MODELS Dislocation Slip Displacive Transformations Damage HOMOGENIZATION Introduction Statistical Representation of Crystallographic Texture Computational Homogenization Mean-Field Homogenization Grain-Cluster Methods NUMERICAL ASPECTS OF CRYSTAL PLASTICITY FINITE ELEMENT METHOD IMPLEMENTATIONS General Remarks Explicit Versus Implicit Integration Methods Element Types PART III: Application MICROSCOPIC AND MESOSCOPIC EXAMPLES Introduction to the Field of CPFE Experimental Validation Stability and Grain Fragmentation in Aluminum under Plane Strain Deformation Texture and Dislocation Density Evolution in a Bent Single-Crystalline Copper-Nanowire Texture and Microstructure underneath a Nanoindent in a Copper Single Crystal Application of a Nonlocal Dislocation Model Including Geometrically Necessary Dislocations to Simple Shear Tests of Aluminum Single Crystals Application of a Grain Boundary Constitutive Model to Simple Shear Tests of Aluminum Bicrystals with Different Misorientation Evolution of Dislocation Density in a Crystal Plasticity Model Three-Dimensional Aspects of Oligocrystal Plasticity Simulation of Recrystallization Using Micromechanical Results of CPFE Simulations Simulations of Multiphase TRIP Steels Damage Nucleation Example The Grain Size-Dependence in Polycrystal Models MACROSCOPIC EXAMPLES Using Elastic Constants from Ab Initio Simulations for Predicting Textures and Texture-Dependent Elastic Properties of Beta-Titanium Simulation of Earing during Cup Drawing of Steel and Aluminum Simulation of Lankford Values Virtual Material Testing for Sheet Stamping Simulations OUTLOOK AND CONCLUSIONS