David L. McDowell

Microstructure-based fatigue modeling of cast A356-T6 alloy

Abstract High cycle fatigue (HCF) life in cast Al–Mg–Si alloys is particularly sensitive to the combination of microstructural inclusions and stress concentrations. Inclusions can range from large-scale shrinkage porosity with a tortuous surface profile to entrapped oxides introduced during the pour. When shrinkage porosity is controlled, the relevant microstructural initiation sites are often the larger Si particles within eutectic regions. In this paper, a HCF model is introduced which recognizes multiple inclusion severity scales for crack formation. The model addresses the role of constrained microplasticity around debonded particles or shrinkage pores in forming and growing microstructurally small fatigue cracks and is based on the cyclic crack tip displacement rather than linear elastic fracture mechanics stress intensity factor. Conditions for transitioning to long crack fatigue crack growth behavior are introduced. The model is applied to a cast A356-T6 Al alloy over a range of inclusion severities.

In-Plane Stiffness and Yield Strength of Periodic Metal Honeycombs

In-plane mechanical properties of periodic honeycomb structures with seven different cell types are investigated in this paper. Emphasis is placed an honeycambs with relative density between 0.1 and 0.3, such that initial yield is associated with short column compression or bending, occurring prior to elastic buckling. Effective elastic stiffness and initial yield strength of these metal honeycombs under in-plane compression, shear, and diagonal compression (for cell structures that manifest in-plane anisotropy) are reported as functions of relative density. Comparison among different hancycomb structures demonstrates that the diamond cells, hexagonal periodic supercells composed of six equilateral triangles and the Kagome cells have superior in-plane mechanical properties among the set considered.

Stress state dependence of cyclic ratchetting behavior of two rail steels

Cumulative inelastic deformation or ratchetting occurs during cyclic loading in the presence of a mean stress. This problem has received considerable recent attention. The nonlinear kinematic hardening rule originally proposed by Armstrong and Frederick (AF rule) [1966] has been widely used for description of the overall character of hysteresis response during cyclic plasticity. However, this model generally overpredicts cyclic strain accumulation (ratchetting) under asymmetric loading with mean stress (Bower [1987]; Bower & Johnson [1989]; Clement & Guionnet [1985]; Chaboche [1989,1991]; Chaboche & Nouailhas [1989]; McDowell & Lamar [1989]; McDowell [1992]). Moreover, unloading-reloading behavior associated with subcycle events under even uniaxial conditions (Chaboche [1989]) are not adequately represented by the AF rule. The same comments apply to other nonlinear kinematic hardening rules of equivalent or similar nature such as bounding surface plasticity theory (cf. McDowell & Moyar [1991]). In this work, a modification of the dynamic recovery term of the AF rule is considered as recently proposed by Ohno and Wang [1991a,1991b]. The approach is established based on certain assumed crystalline slip system behavior and interaction between dislocation interactions at different size scales. Several important criteria are discussed for models capable of representing stress state and amplitude dependence of ratchetting behavior. Experimental results obtained on both a carbon rail steel and a heat-treated rail steel subjected to various uniaxial and nonproportional loading conditions are presented and correlated with an extension of the Ohno and Wang model, which accounts for a broader range of stress state and amplitude effects. An algorithm is developed to extrapolate the ratchetting rates obtained at relatively early cycles to very large numbers of cycles for test specimens. The method provides for dependence on the mean stress as well as amplitude of loading. The algorithm is applied to both carbon and heat-treated rail steels.

Mechanical Behavior of an Ni-Ti Shape Memory Alloy Under Axial-Torsional Proportional and Nonproportional Loading

Several biaxial proportional and nonproportional loading experiments are reported for thin-wall tubes of a pseudoelastic Ni-Ti shape memory alloy (SMA). In addition to the mechanical behavior, temperature was measured during the experiments. It is shown that the phase transformation exhibits asymmetrical behavior in the case of tension-compression cycling. The transformation strain rate is determined for selected histories by numerical differentiation of data. Under nonproportional loading, the rate of phase transformation does not follow a generalized J{sub 2}-J{sub 3} criteria based on results of micromechanical simulations for proportional loading. The role of simultaneous forward and reverse transformations on the nonproportional transformation response is examined using a simple micromechanical model, and the direction of the inelastic strain rate is adequately predicted. Load- and strain-controlled experiments at different strain rates, with and without hold times, are reported and coupled thermomechanical effects are studied.

Asymmetric tilt grain boundary structure and energy in copper and aluminium

Atomistic simulations were employed to investigate the structure and energy of asymmetric tilt grain boundaries in Cu and Al. In this work, we examine the Σ5 and Σ13 systems with a boundary plane rotated about the ⟨ 100 ⟩ misorientation axis, and the Σ9 and Σ11 systems rotated about the ⟨ 110 ⟩ misorientation axis. Asymmetric tilt grain boundary energies are calculated as a function of inclination angle and compared with an energy relationship based on faceting into the two symmetric tilt grain boundaries in each system. We find that asymmetric tilt boundaries with low index normals do not necessarily have lower energies than boundaries with similar inclination angles, contrary to previous studies. Further analysis of grain boundary structures provides insight into the asymmetric tilt grain boundary energy. The Σ5 and Σ13 systems in the ⟨ 100 ⟩ system agree with the aforementioned energy relationship; structures confirm that these asymmetric boundaries facet into the symmetric tilt boundaries. The Σ9 and Σ11 systems in the ⟨ 110 ⟩ system deviate from the idealized energy relationship. As the boundary inclination angle increases towards the Σ9 (221) and Σ11 (332) symmetric tilt boundaries, the minimum energy asymmetric boundary structures contain low index {111} and {110} planes bounding the interface region.

Structures and energies of Σ 3 asymmetric tilt grain boundaries in copper and aluminium

The objective of this research is to use atomistic simulations to investigate the energy and structure of symmetric and asymmetric Σ3 ⟨110⟩ tilt grain boundaries. A nonlinear conjugate gradient algorithm was employed along with an embedded atom method potential for Cu and Al to generate the equilibrium 0 K grain boundary structures. A total of 25 ⟨110⟩ grain boundary structures were explored to identify the various equilibrium and metastable structures. Simulation results show that the Σ3 asymmetric tilt grain boundaries in the ⟨110⟩ system are composed of only structural units of the two Σ3 symmetric tilt grain boundaries. The energies for the Σ3 grain boundaries are similar to previous experimental and calculated grain boundary energies. A structural unit and faceting model for Σ3 asymmetric tilt grain boundaries fits all of the calculated asymmetric grain boundary structures. The significance of these results is that the structural unit and facet description of all Σ3 asymmetric tilt grain boundaries may be predicted from the structural units of the Σ3 coherent twin and incoherent twin boundaries for both Cu and Al.

Key computational modeling issues in Integrated Computational Materials Engineering

Designing materials for targeted performance requirements as required in Integrated Computational Materials Engineering (ICME) demands a combined strategy of bottom-up and top-down modeling and simulation which treats various levels of hierarchical material structure as a mathematical representation, with infusion of systems engineering and informatics to deal with differing model degrees of freedom and uncertainty. Moreover, with time, the classical materials selection approach is becoming generalized to address concurrent design of microstructure or mesostructure to satisfy product-level performance requirements. Computational materials science and multiscale mechanics models play key roles in evaluating performance metrics necessary to support materials design. The interplay of systems-based design of materials with multiscale modeling methodologies is at the core of materials design. In high performance alloys and composite materials, maximum performance is often achieved within a relatively narrow window of process path and resulting microstructures. Much of the attention to ICME in the materials community has focused on the role of generating and representing data, including methods for characterization and digital representation of microstructure, as well as databases and model integration. On the other hand, the computational mechanics of materials and multidisciplinary design optimization communities are grappling with many fundamental issues related to stochasticity of processes and uncertainty of data, models, and multiscale modeling chains in decision-based design. This paper explores computational and information aspects of design of materials with hierarchical microstructures and identifies key underdeveloped elements essential to supporting ICME. One of the messages of this overview paper is that ICME is not simply an assemblage of existing tools, for such tools do not have natural interfaces to material structure nor are they framed in a way that quantifies sources of uncertainty and manages uncertainty in representing physical phenomena to support decision-based design.

Behavior of a random hollow sphere metal foam

Abstract The quasistatic uniaxial compression behavior of both single hollow spheres and bulk metal foams comprised of the same hollow spheres is examined experimentally. The spheres are nominally the composition of a 405 stainless steel (Fe–12Cr), with a 2 mm outside diameter and 0.1 mm thick walls, and are sintered together to process the bulk foam. It is shown that to first order the bulk foam stress–strain behavior, Poisson effects, and densification may be understood on the basis of simple experiments performed on single spheres between parallel platens. These hollow sphere foams appear to behave similar to open-cell foams. Finite element modeling of finite compression of a single sphere lends further insight into the deformation process and the role of plastic bending and contact of cell walls during the process of densification.

Basic issues in the mechanics of high cycle metal fatigue

Mechanics issues related to the formation and growth of cracks ranging from subgrain dimension to up to the order of one mm are considered under high cycle fatigue (HCF) conditions for metallic materials. Further efforts to improve the accuracy of life estimation in the HCF regime must consider various factors that are not presently addressed by traditional linear elastic fracture mechanics (LEFM) approaches, nor by conventional HCF design tools such as the S-N curve, modified Goodman diagram and fatigue limit. A fundamental consideration is that a threshold level for ΔK for small/short cracks may be considerably lower than that for long cracks, leading to non-conservative life predictions using the traditional LEFM approach.Extension of damage tolerance concepts to lower length scales and small cracks relies critically on deeper understanding of (a) small crack behavior including interactions with microstructure, (b) heterogeneity and anisotropy of cyclic slip processes associated with the orientation distribution of grains, and (c) development of reliable small crack monitoring techniques. The basic technology is not yet sufficiently advanced in any of these areas to implement damage tolerant design for HCF. The lack of consistency of existing crack initiation and fracture mechanics approaches for HCF leads to significant reservations concerning application of existing technology to damage tolerant design of aircraft gas turbine engines, for example. The intent of this paper is to focus on various aspects of the propagation of small cracks which merit further research to enhance the accuracy of HCF life prediction. Predominant concern will rest with polycrystalline metals, and most of the issues pertain to wide classes of alloys.

A nonlinear kinematic hardening theory for cyclic thermoplasticity and thermoviscoplasticity

Abstract The multiple backstress nonlinear kinematic hardening model of Moosbrugger and McDowell [1990] is extended to thermomechanical cyclic loading conditions. The model employs a decomposition of the isotropic hardening between the yield surface and backstress saturation amplitudes, with certain components independent of the degree of isotropic hardening. General forms are presented for thermoplasticity and thermoviscoplasticity that include temperature rate terms in both the kinematic and isotropic hardening parameters. General forms are presented for temperature path history-dependent and -independent materials; it is shown that the latter case is an important feature in thermoplasticity, since the flow rule cannot exhibit the necessary degree of temperature dependence. In the thermoviscoplastic case, the rate-dependence is decomposed between the flow rule and backstress saturation amplitudes, a unique feature consistent with dislocation cross slip. Thermodynamical restrictions are discussed for both cases, and isothermal and nonisothermal cyclic loading experiments are correlated with both theories.