Modeling high-temperature stress-strain behavior of cast aluminum alloys

A modified two-state-variable unified constitutive model is presented to model the high-temperature stress-strain behavior of a 319 cast aluminum alloy with a T7 heat treatment. A systematic method is outlined, with which one can determine the material parameters used in the experimentally based model. The microstructural processes affecting the material behavior were identified using transmission electron microscopy and were consequently correlated to the model parameters. The stress-strain behavior was found to be dominated by the decomposition of the metastable θ′ precipitates within the dendrites and the subsequent coarsening of the θ phase, which was manifested through remarkable softening with cycling and time. The model was found to accurately simulate experimental stress-strain behavior such as strain-rate sensitivity, cyclic softening, aging effects, transient material behavior, and stress relaxation, in addition to capturing the main deformation mechanisms and microstructural changes as a function of temperature and inelastic strain rate.     

Predicting twinning stress in fcc metals: Linking twin-energy pathways to twin nucleation

Deformation twinning is observed in numerous engineering and naturally occurring materials. However, a fundamental law for critical twinning stress has not yet emerged. We resolve this long-standing issue by integrating twin-energy pathways obtained via ab initio density functional theory with heterogeneous, dislocation-based twin nucleation models. Through a hierarchical theory, we establish an analytical expression that quantitatively predicts the critical twinning stress in face-centered cubic metals without any empiricism at any length scale. Our theory predicts a monotonic relation between the unstable twin stacking fault energy and twin nucleation stress revealing the physics of twinning.     

Fatigue crack growth in Haynes 230 single crystals: an analysis with digital image correlation

Fatigue crack growth was investigated in Haynes 230, a nickel‐based superalloy. Anisotropic stress intensity factors were calculated with a least squares algorithm using the displacements obtained from digital image correlation. Crack opening/sliding levels were measured by analysing the relative displacement of crack flanks. Reversed crack tip plastic zones were calculated adopting an anisotropic yield criterion. The strains measured in the reversed plastic zone by digital image correlation showed a dependence on crystallographic orientation. Finally, a finite element model was adopted to examine plasticity around the crack tip. Results were compared with the experimentally observed strains.     

Deformation of NiTiCu shape memory single crystals in compression

Single-crystal orientations of NiTi10Cu alloys were studied under incremental, cyclic compression conditions to establish the pseudoelastic and shape memory response of this class of alloys. This material exhibits a two-step transformation involving cubic to orthorhombic martensite (B2 → B19) followed by orthorhombic to monoclinic martensite (B19 → B19′). The transformation parameters (shear magnitudes and directions for habit and twin planes) were determined associated with the B2 → B19 transformation. The growth of monoclinic martensite correspondent variant pairs (CVPs) emanating from the orthorhombic structure was also analyzed. The transformation strain for the B2 → B19 case was orientation dependent and lower than the B19 → B19′ transformation in compression for all orientations except those near the [001] pole. The experimental results show that the critical transformation stress is orientation dependent and is in the range 30 to 58 MPa. Orientations that exhibit lower transformation stress (or high resolved shear stress factors, [100] and [012]) produce higher recoverable strains (as high as 4 pct), while other orientations ([011], [111], and [123]) with lower resolved shear stress factors result in recoverable strains less than 3 pct. At higher strains, inelastic deformation develops, limiting recoverability. The recoverable strains are lower than the theoretical values for two main reasons: the transformation is curtailed first by austenite slip and subsequently by martensite slip, and the orthorhombic structure does not fully transform to the monoclinic martensite.     

Analysis of multistep transformations in single-crystal NiTi

The effects of composition and heat treatment on the thermally induced phase-transformation behavior of single-crystal NiTi with compositions of 50.1, 50.4, 50.8, and 51.5 at. pct Ni are presented in this article. Differential scanning calorimetry (DSC) experiments reveal that a heat-treated 50.1 at. pct Ni alloy exhibits an unprecedented multiple-step transformation (MST) on both heating and cooling, with up to four peaks. This behavior is absent in the higher-Ni-content alloys. In polycrystalline NiTi alloys, MSTs have been attributed to microstructure heterogeneities such as grain boundaries and dislocations, which influence precipitation. In-situ scanning electron microscopy (SEM) results show that the MST in the 50.1 at. pct Ni alloy is associated with single-crystal defects such as dendrites and low-angle boundaries. A heterogeneous precipitate distribution is observed in transmission electron microscopy (TEM) images of the same low-Ni alloy, also associated with the defects, creating conditions that have been shown in other studies to promote the MST in polycrystals. These MSTs are not observed for high-Ni single-crystal alloys containing the same defects. In this article, we describe the origin of the extraordinary forward and reverse MSTs in the low-Ni alloy and the absence of the MST in high-Ni alloys. Transformation sequences are proposed based on the contrasting precipitate microstructures.     

Modeling of fatigue crack closure in inclined and deflected cracks

A 2-dimensional, elastic-plastic finite element model has been developed to simulate plasticity induced crack closure in slanted and deflected cracks growing outside the small scale yielding (SSY) regime. The finite element model allows for contact between deformable surfaces to capture the complex contact interaction between the crack faces. Coulomb's friction law has been used to model friction between the crack faces and has been incorporated in the finite element model. This paper examines the mode I and mode II behavior of slanted cracks subjected to remote mode I, constant amplitude cyclic loading. Two possible types of mode II crack face interaction have been identified: (a) complete slip in mode II before mode I opening and, (b) mode I crack opening before the crack faces undergo mode II displacements. Both types of interactions were observed in slanted cracks. The finite element study also reveals a clear dependence of mode I and mode II crack opening levels for a slanted crack on R ratio and maximum stress, S_max/₀. The crack opening levels for a slanted crack are found to be significantly higher than the stable opening values for a straight crack growing in pure mode I. The mode I and mode II crack opening levels are also found to depend on the friction between the crack faces. A four-fold increase in friction coefficient resulted in almost 50% increase in normalized mode I and mode II opening values. This paper also describes the effect of crack deflection on closure. Deflection of a fatigue crack from 45° inclination to pure mode I caused a decrease in mode I opening level, but, an increase in mode II opening level. This difference in opening behavior is attributed to the transition of the nature of crack interaction from complete slip before opening to opening in mode I before mode II shear offset. Final stable opening levels for a deflected crack are found to be close to the stable value for straight cracks.     

Detwinning in NiTi alloys

This work focuses on the stress-induced transformation in solutionized and overaged single-crystal NiTi alloys. The potential role of detwinning on the recoverable strains was investigated both theoretically and also with temperature-cycling experiments. The detwinning is the growth of one variant within a martensite in expense of the other. It is shown that the experimental recoverable strains in tension (near 8.01 pct in the [123], 9.34 pct in the [111], and 7.8 pct in the [011] orientations) exceed the theoretical martensite (correspondent-variant pair (CVP) formation strains (6.49 pct in [123], 5.9 pct in [111], and 5.41 pct in [011]), lending further support that partial detwinning of martensite has occurred in both the solutionized and overaged specimens. In compression, the experimental recoverable strains are lower than the theoretical martensite (CVP) formation strain. In the compression cases, the detwinning strain contribution is calculated to be negligible in most orientations. The transformation strains observed in overaged NiTi are similar to the solutionalized NiTi, suggesting that incoherent precipitates do not restrict the detwinning of the martensite. For the [123] orientation, it is demonstrated that the thermal hysteresis is higher in solutionized NiTi compared to the overaged NiTi. The higher thermal hysteresis can be exploited in applications involving damping and shape stability, while the lower hysteresis is suited for actuators.     

Energy landscape for martensitic phase transformation in shape memory NiTi

First-principles calculations are presented for parent B2 phase and martensitic B19 and B19′ phases in NiTi. The results indicate that both B19 and B19′ are energetically more stable than the parent B2 phase. By means of ab initio density functional theory, the complete distortion–shuffle energy landscape associated with B2 → B19 transformation in NiTi is then determined. In addition to accounting for the Bain-type deformation through the Cauchy–Born rule, the study explicitly accounts for the shuffle displacements experienced by the internal ions in NiTi. The energy landscape allows the energy barrier associated with the B2 → B19 transformation pathway to be identified. The results indicate that a barrier of 0.48 mRyd atom^?1 (relative to the B2 phase) must be overcome to transform the parent B2 NiTi to orthorhombic B19 martensite.