Microstructural Length Research Articles

Fatigue crack growth and fracture behavior of as-cast Ti-43.5Al-4Nb-1Mo-0.1B (TNM) compared to Ti-48Al-2Nb-2Cr (4822)

The effects of sample orientation and load ratio on the room-temperature fatigue crack growth and fracture behavior of a third-generation gamma titanium aluminide Ti-43.5Al-4Nb-1Mo-0.1B (TNM) were determined and compared with that of a second-generation alloy Ti-48Al-2Nb-2Cr (4822). Both materials are currently used as low pressure turbine blades in fuel-efficient gas turbine engines. Bend bar specimens, excised from the as-cast articles in the longitudinal and transverse directions to the casting direction, were tested at room temperature in lab air. Load ratios in the range 0.1–0.9 were used in fatigue testing to determine their effects on the fatigue threshold, Paris law slope, and stress intensity at overload in fatigue. Microscopy and fractography were used to document the effects of sample orientation on the fatigue crack path and morphology. Significant effects of changes in load ratio were observed on the fatigue threshold and Paris law slope, while effects of sample orientation were minimal for both alloys. The effects of microstructure length scale and differences in micro-constituents are discussed in relation to the properties measured.

Sea urchin growth dynamics at microstructural length scale revealed by Mn-labeling and cathodoluminescence imaging

BackgroundFluorochrome staining is among the most widely used techniques to study growth dynamics of echinoderms. However, it fails to detect fine-scale increments because produced marks are commonly diffusely distributed within the skeleton. In this paper we investigated the potential of trace element (manganese) labeling and subsequent cathodoluminescence (CL) imaging in fine-scale growth studies of echinoderms.ResultsThree species of sea urchins (Paracentrotus lividus, Echinometra sp. and Prionocidaris baculosa) were incubated for different periods of time in seawater enriched in different Mn2+ concentrations (1 mg/L; 3 mg/L; 61.6 mg/L). Labeling with low Mn2+ concentrations (at 1 mg/L and 3 mg/L) had no effect on behavior, growth and survival of sea urchins in contrast to the high Mn2+ dosage (at 61.6 mg/L) that resulted in lack of skeleton growth. Under CL, manganese produced clearly visible luminescent growth fronts in these specimens (observed in sectioned skeletal parts), which allowed for a determination of the average extension rates and provided direct insights into the morphogenesis of different types of ossicles. The three species tend to follow the same patterns of growth. Spine growth starts with the formation of microspines which are simultaneously becoming reinforced by addition of thickening layers. Spine septa develop via deposition of porous stereom that is rapidly (within less than 2 days) filled by secondary calcite. Development of the inner cortex in cidaroids begins with the formation of microspines which grow at ~3.5 μm/day. Later on, deposition of the outer polycrystalline cortex with spinules and protuberances proceeds at ~12 μm/day. The growth of tooth can be rapid (up to ~1.8 mm/day) and starts with the formation of primary plates (pp) in plumula. Later on, during the further growth of pp in aboral and lateral directions, secondary extensions develop inside (in chronological order: lamellae, needles, secondary plate, prisms and carinar processes), which are increasingly being solidified towards the incisal end. Interradial growth in the ambital interambulacral test plates exceeds meridional growth and inner thickening.ConclusionsMn2+ labeling coupled with CL imaging is a promising, low-cost and easily applicable method to study growth dynamics of echinoderms at the micro-length scale. The method allowed us to evaluate and refine models of echinoid skeleton morphogenesis.

Wave propagation through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces

Reflection and transmission of plane waves through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces are studied in this paper. The secular equations in the flexoelectric piezoelectric material are first derived from the general governing equation. Different from the classical piezoelectric medium, there are five kinds of coupled elastic waves in the piezoelectric material with the microstructure effects taken into consideration. The state vectors are obtained by the summation of contributions from all possible partial waves. The state transfer equation of flexoelectric piezoelectric slab is derived from the motion equation by the reduction of order, and the transfer matrix of flexoelectric piezoelectric slab is obtained by solving the state transfer equation. By using the continuous conditions at the interface and the approach of partition matrix, we get the resultant algebraic equations in term of the transfer matrix from which the reflection and transmission coefficients can be calculated. The amplitude ratios and further the energy flux ratios of various waves are evaluated numerically. The numerical results are shown graphically and are validated by the energy conservation law. Based on these numerical results, the influences of two characteristic lengths of microstructure and the flexoelectric coefficients on the wave propagation are discussed.

V-notch tip subjected to in-plane mixed mode loading: overview of recent results and possible future outcomes

The fictitious notch rounding concept is applied for the first time to V-notches with root hole subjected to in-plane mixed mode loading. Outof- bisector crack propagation is taken into account. The fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been used. It is combined with the maximum tangential stress criterion to determine the crack propagation angle. An analytical method based on Neuber's procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. Finally, for comparison, the support factor is determined on a purely numerical basis by iterative analysis of FE models.

The effects of Zn segregation and microstructure length scale on the corrosion behavior of a directionally solidified Mg-25 wt.%Zn alloy

Biodegradable implants can be used in order to avoid removal surgery. Mg-Zn alloys are considered interesting alternatives for biomedical applications, however, studies concerning the effects of microstructural features in the as-solidified condition and segregation aspects on the resulting electrochemical behavior are scarce. This investigation is focused on the evaluation of the electrochemical corrosion of an as-solidified Mg-25 wt.% Zn alloy in a 0.15 M NaCl solution at 25 °C. EIS plots, potentiodynamic polarization curves and equivalent circuits are used. It is shown that Zn segregation affects both the galvanic couple and the cathode-to-anode area ratio. It was found that finer and homogeneously distributed Mg-rich six-fold branched equiaxed dendritic grains induce lower corrosion current density and higher polarization resistance when compared with equivalent results of coarser ones.

Interrelation of Solidification Processing Variables and Microstructure of a Horizontally Solidified Al-based 319.1 Alloy

In this paper, primary ( λ 1 ) and tertiary ( λ 3 ) dendritic arm spacings of a ternary Al – 7wt.% Si – 3 wt.% Cu alloy casting were characterized and correlated with solidification processing variables: growth rates (V L ), cooling rates (T C ) as well as local solidification times (t SL ). Horizontal directional solidification experiments were carried out under transient heat extraction undergoing cooling rates varying from 0.9 o C/s to 22 o C/s to be associated with samples having quite different microstructural length parameters. Techniques of metallography and optical microscopy were applied in order to have λ 1 and λ 3 measured. The obtained as-cast microstructures consisted of dendritic α-Al, with Si particles in the aluminum-rich matrix as well distributed along the interdendritic regions in the eutectic mixture interlinked with θ (Al 2 Cu) intermetallic phase developing the microstructure α -Al + θ + Si. The results showed that power laws – 1.1, – 0 .55 and 0.55 express the variations of both λ 1 and λ 3 with V L , T C and t SL , respectively, for investigated alloy. A comparative study with the Al – 3wt.% Cu alloy from literature was also performed and the results show that the growth law of λ 1 as a function of T C is represented, for both the investigated alloys, by the mathematical expression given by λ 1 = constant (T C ) -0.55 . DOI: http://dx.doi.org/10.5755/j01.ms.23.2.15768

The Theory of Critical Distances: A link to micromechanisms

The Theory of Critical Distances (TCD) is a methodology for prediction of the effect of stress concentration features on material failure, especially cracking-related mechanisms such as fatigue and brittle fracture. It has a long history but has become much more relevant to industrial problems in recent years thanks to the widespread availability of finite element analysis and other numerical simulation tools. An ongoing fundamental challenge is to understand the physical significance of the TCD parameters, in particular the value of the critical length L, in relation to the underlying micromechanisms of crack extension and toughening. A novel approach is presented here, in which the TCD is used to make predictions of the notch fracture behaviour of three different model materials having different crack extension mechanisms. Three different notch types (circular holes, long slots and short cracks) were investigated. In all cases the value of L was shown to be simply related to a microstructural length parameter but this relationship depended on the mechanism involved. These results provide some insights into the distinctive behaviour of different materials, especially polymers such as PMMA which display crazing behaviour, and fibre composites such as carbon/epoxy laminates.

Oxidation mechanism of W substituted Mo-Si-B alloys

The oxidation mechanism of a Mo55W15Si15B15 alloy was established, and the effects of W content, oxidation temperature and microstructural length scale were determined. In addition to influencing the oxidation mechanism, the addition of W also destabilized the A15 phase which is consistent with our previous experiments in ternary Mo-W-Si alloys [1]. Microstructural investigation of the oxidized alloy revealed entrapped tungsten oxides at temperatures below 1300 °C, which volatilize above 1400–1500 °C. The presence of WO3 in the oxide scale interrupts the surface coverage by the glassy borosilicate, thereby adversely affecting the oxidation behavior. In order to determine the effects of length scale, the microstructural evolution during the transient oxidation of cast and sintered alloys, with different microstructural length scales, was studied at 1100 and 1400 °C. Finer microstructure promoted faster borosilicate surface coverage at 1400 °C.

Pretwisted beam subjected to thermal loads: A gradient thermoelastic analogue

ABSTRACTIt is well known from the classical torsion theory that the cross section of a prismatic beam subjected to end torsional moments will rotate and warp in the longitudinal direction. Rotation is depicted through the angle of twist per unit length and depends in general on the position along the length of the beam, while the warping function addresses the longitudinal distortion of the unrotated cross sections. In the present study, we consider a prismatic beam that possesses an initial twist which is constant along its length. A thermal field is present along the beam and its ends are loaded with axial forces and torsional moments. The governing equilibrium equations and the corresponding boundary conditions were obtained using an energy variational statement. A one-dimensional gradient thermoelastic analogue is developed. The advantageous aspect of the present study is that the additional (and peculiar) boundary conditions required by the gradient elasticity theory and the related microstructural lengths, analogous to micromechanical lengths, emerge in a natural way from the geometrical characteristics of the beam cross section and the material properties. We have examined various examples with different cross sections and loads to demonstrate the applicability of the model to the design of special yarns useful in smart textiles and thermally activated microdrilling actuators.

Wettability and Contact Time on a Biomimetic Superhydrophobic Surface.

Inspired by the array microstructure of natural superhydrophobic surfaces (lotus leaf and cicada wing), an array microstructure was successfully constructed by high speed wire electrical discharge machining (HS-WEDM) on the surfaces of a 7075 aluminum alloy without any chemical treatment. The artificial surfaces had a high apparent contact angle of 153° ± 1° with a contact angle hysteresis less than 5° and showed a good superhydrophobic property. Wettability, contact time, and the corresponding superhydrophobic mechanism of artificial superhydrophobic surface were investigated. The results indicated that the micro-scale array microstructure was an important factor for the superhydrophobic surface, while different array microstructures exhibited different effects on the wettability and contact time of the artificial superhydrophobic surface. The length (L), interval (S), and height (H) of the array microstructure are the main influential factors on the wettability and contact time. The order of importance of these factors is H > S > L for increasing the apparent contact angle and reducing the contact time. The method, using HS-WEDM to fabricate superhydrophobic surface, is simple, low-cost, and environmentally friendly and can easily control the wettability and contact time on the artificial surfaces by changing the array microstructure.

A robust inverse analysis method to estimate the local tensile properties of heterogeneous materials from nano-indentation data

Most current analysis of nano-indentation test data assumes the sample to behave as an isotropic, homogeneous body. In practice, engineering materials such as structural steels, titanium alloys and high strength aluminium alloys are multi-phase metals with microstructural length scales that can be the same order of magnitude as the maximum achievable nano-indentation depth. This heterogeneity results in considerable scatter in the indentation load-displacement traces and complicates inverse analysis of this data. To address this problem, an improved and optimised inverse analysis procedure to estimate bulk tensile properties of heterogeneous materials using a new ‘multi-objective’ function has been developed which considers nano-indentation data obtained from several indentation sites. The technique was applied to S355 structural steel bulk samples as well as an autogenously electron beam welded sample where there is a local variation of material properties. Using the new inverse analysis approach on the S355 bulk material resulted in an error within 3% of the experimental yield strength and strain hardening exponent data, which compares to an approximate 9% error in the yield strength and an 8% error in the strain hardening exponent using a more conventional approach to the inverse analysis method. Applying the new method to indentation data from different regions of an S355 steel weld and using this data as an input into an FE model of the cross-weld, tensile data from the FE model resulted matching the experimentally measured properties to within 5%, confirming the efficacy of the new inverse analysis approach.

Toward a better understanding of conjugated polymer blends with non-spherical small molecules: coupling of molecular structure to polymer chain microstructure

Abstract

Texture-dependent character of strain heterogeneity in Magnesium AZ31 under reversed loading

Depending on operational micromechanisms and crystallographic texture, the innate strain localization at microstructural length scales of a polycrystal can spatially coordinate to induce macroscopic strain localization. A challenge for material performance and modeling, this behavior is observed in wrought Magnesium alloys when they deform with heavy tensile twinning. With in-situ, multi-surface image correlation, a compression-tension experiment is implemented on samples with extrusion and rolling texture that have a consistent 11µm grain size. While samples of both textures exhibit a clear twin plateau with close stress levels (90/99MPa for rolled/extruded samples), the strain localization patterns are vastly different, both in terms of geometric structure and intensity. Rolled sample exhibits sharp shear banding structures with a fixed plane of shear. Extruded sample exhibits strain localization that is not in macroscopic ±45° shear form and much weaker in intensity (by about a factor of 2). Once the load is reversed and the tensile twin is deactivated, strain accommodation largely homogenizes for both textures during detwinning and subsequent high hardening stages.

Different composite voxel methods for the numerical homogenization of heterogeneous inelastic materials with FFT-based techniques

FFT-based homogenization methods aim at calculating the effective behavior of heterogeneous materials with periodic microstructures. These methods operate on a regular grid of voxels, and hence require an appropriate spatial discretization of periodic microstructures. However, when different microstructural length scales are involved, it is not always possible to have sufficient spatial resolutions to explicitly consider the influence of fine microstructural features (e.g. voids, second-phase particles). To circumvent this difficulty, one solution consists of using composite voxel methods to define the effective properties and the effective internal variables of heterogeneous voxels.In this work, different composite voxel methods are proposed to deal with inelastic materials with multiple length scales. These methods use simple homogenization rules to calculate the effective behavior of heterogeneous voxels. The first part of this paper is dedicated to the description of the composite voxel methods, which are based either on the Voigt, laminate structure or Mori–Tanaka approximations. In the second part, these methods are used to model the elasto-plastic behavior of a pearlitic steel polycrystalline aggregate. According to the results, the Voigt approximation, which ignores morphological features, is not appropriate for treating heterogeneous voxels. When morphological information is accounted for, with either the laminate structure or Mori–Tanaka approximations, a better agreement with experimental observations is obtained. Though none of these methods is universal, they offer some possibilities to investigate the mechanical behavior of heterogeneous materials involving multiple length scales.

Unusual strain rate sensitivity of nanoscale amorphous CuZr/crystalline Cu multilayers

Nanoscale amorphous CuZr/crystalline Cu multilayers were synthesized to study their strain rate sensitivity and plastic deformation mechanisms via nanoindentation testing. Despite the dramatically reduced microstructural length scale, nearly constant strain rate sensitivity of the multilayers was obtained at a wide range of individual layer thickness (10~100nm). The scenarios that the two constituent layers mutually confined by each other might exhibit quite different strain rate sensitivities relative to the monolithic ones were proposed. Specifically, compared with the monolithic Cu and CuZr layers, respectively, the confined Cu layers should exhibit gentler increases in strain rate sensitivity while confined CuZr layers exhibit reduced strain rate sensitivity, as Cu layer thickness decreases. Correspondingly, corresponding deformation mechanisms accommodating the co-deformation of the two constituent layers were discussed in detail.

Dendritic evolution during coarsening of Mg-Zn alloys via 4D synchrotron tomography

The scale of solidification microstructures directly impacts micro-segregation, grain size, and other factors which control strength. Using in situ high speed synchrotron X-ray tomography we have directly quantified the evolution of dendritic microstructure length scales during the coarsening of Mg-Zn hcp alloys in three spatial dimensions plus time (4D). The influence of two key parameters, solute composition and cooling rate, was investigated. Key responses, including specific surface area, dendrite mean and Gauss curvatures, were quantified as a function of time and compared to existing analytic models. The 3D observations suggest that the coarsening of these hcp dendrites is dominated by both the re-melting of small branches and the coalescence of the neighbouring branches. The results show that solute concentration has a great impact on the resulting microstructural morphologies, leading to both dendritic and seaweed-type grains. It was found that the specific solid/liquid surface and its evolution can be reasonably scaled to time with a relationship of ∼ t−1/3. This term is path independent for the Mg-25 wt%Zn; that is, the initial cooling rate during solidification does not greatly influence the coarsening rate. However, path independence was not observed for the Mg-38 wt%Zn samples because of the seaweed microstructure. This led to large differences in the specific surface area (Ss) and its evolution both between the two alloy compositions and within the Mg-38 wt%Zn for the different cooling rates. These findings allow for microstructure models to be informed and validated to improve predictions of solidification microstructural length scales and hence strength.

A review of the notch rounding approach under in plane mixed mode loading

The fictitious notch rounding approach is widely used for the fatigue assessment of welded joints and for this reason in the present paper a review of the concept applied to inclined lateral V-notches with root hole subjected to in-plane mixed mode loading has been carried out. This is the basis for future applications to welded structures in presence of mixed mode loading.The analytical framework of the method is herein recalled and the fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. In order to reduce the complexity of the task, we adopt a method based on the normal stress failure criterion. The method provides the values of the microstructural support factor as a function of the mode mixity parameter and the notch-opening angle. Moreover, the support factor is assumed independent of the microstructural support length. Finite element simulations for various notch shape and configurations are compared to experimental data from pointed V-notches made of polymethylmethacrylate. The model prediction showed good agreement with the experimental results. These results are very promising for the application to welded structures.

Application of Neuber’s effective stress method for the evaluation of the fatigue behaviour of magnesium welds

In this study, the microstructural length of magnesium welded joints was determined by using experimental data acquired from three different weld geometries and Neuber’s stress averaging method. The aim was to determine microstructural length, which is assumed to be a material constant that is identical for all Mg-materials, so that it can be employed for effective stress and fictitious notch radius rf calculations. By considering the worst case scenario, rreal=0, this fictitious notch radius can be used as a new reference radius rref for magnesium welded joints.Using the reference radii from two different hypotheses rref=1mm and rref=0.05mm, calculations were performed for notches and data were employed in the calculations. Also FE-analyses were utilised in order to identify the stress gradients for weld geometries. Effective stresses were calculated using experimental data along with the stress gradients in Neuber’s stress averaging method.Finally, S-N lines were derived by correlating effective stresses with fatigue life for the worst case with R=0.5 to account for possible high tensile residual stresses. The scatters of these S-N lines were calculated and compared for every ρ∗ iteration. The length value that resulted in the minimum scatter corresponded to the microstructural length. The identified microstructural length was ρ∗=0.12mm. Until now, there were no published results for microstructural length of magnesium welded joints and the findings in this paper can be used to replace the current recommendations regarding magnesium welded joints.

In situ observation of strain and phase transformation in plastically deformed 301 austenitic stainless steel

To inform the design of superior transformation-induced plasticity (TRIP) steels, it is important to understand what happens at the microstructural length scales. In this study, strain-induced martensitic transformation is studied by in situ digital image correlation (DIC) in a scanning electron microscope. Digital image correlation at submicron length scales enables mapping of transformation strains with high confidence. These are correlated with electron backscatter diffraction (EBSD) prior to and post deformation process to get a comprehensive understanding of the strain-induced transformation mechanism. The results are compared with mathematical models for enhanced prediction of strain-induced martensitic phase transformation.

Combinatorial Strategies for Synthesis and Characterization of Alloy Microstructures over Large Compositional Ranges.

The exploration of new alloys with desirable properties has been a long-standing challenge in materials science because of the complex relationship between composition and microstructure. In this Research Article, we demonstrate a combinatorial strategy for the exploration of composition dependence of microstructure. This strategy is comprised of alloy library synthesis followed by high-throughput microstructure characterization. As an example, we synthesized a ternary Au-Cu-Si composition library containing over 1000 individual alloys using combinatorial sputtering. We subsequently melted and resolidified the entire library at controlled cooling rates. We used scanning optical microscopy and X-ray diffraction mapping to explore trends in phase formation and microstructural length scale with composition across the library. The integration of combinatorial synthesis with parallelizable analysis methods provides a efficient method for examining vast compositional ranges. The availability of microstructures from this vast composition space not only facilitates design of new alloys by controlling effects of composition on phase selection, phase sequence, length scale, and overall morphology, but also will be instrumental in understanding the complex process of microstructure formation in alloys.