High-entropy alloys are equiatomic, multi-element systems that can crystallize as a single phase, despite containing multiple elements with different crystal structures. A rationale for this is that the configurational entropy contribution to the total free energy in alloys with five or more major elements may stabilize the solid-solution state relative to multiphase microstructures. We examined a five-element high-entropy alloy, CrMnFeCoNi, which forms a single-phase face-centered cubic solid solution, and found it to have exceptional damage tolerance with tensile strengths above 1 GPa and fracture toughness values exceeding 200 MPa·m(1/2). Furthermore, its mechanical properties actually improve at cryogenic temperatures; we attribute this to a transition from planar-slip dislocation activity at room temperature to deformation by mechanical nanotwinning with decreasing temperature, which results in continuous steady strain hardening.

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A fracture-resistant high-entropy alloy for cryogenic applications

High-entropy alloys are an intriguing new class of metallic materials that derive their properties from being multi-element systems that can crystallize as a single phase, despite containing high concentrations of five or more elements with different crystal structures. Here we examine an equiatomic medium-entropy alloy containing only three elements, CrCoNi, as a single-phase face-centred cubic solid solution, which displays strength-toughness properties that exceed those of all high-entropy alloys and most multi-phase alloys. At room temperature, the alloy shows tensile strengths of almost 1 GPa, failure strains of ∼70% and KJIc fracture-toughness values above 200 MPa  m(1/2); at cryogenic temperatures strength, ductility and toughness of the CrCoNi alloy improve to strength levels above 1.3 GPa, failure strains up to 90% and KJIc values of 275 MPa  m(1/2). Such properties appear to result from continuous steady strain hardening, which acts to suppress plastic instability, resulting from pronounced dislocation activity and deformation-induced nano-twinning.

/pdf/exceptional-damage-tolerance-of-a-medium-entropy-alloy-1ezzci6auz.pdf

Exceptional damage-tolerance of a medium-entropy alloy CrCoNi at cryogenic temperatures

Physics of inhomogeneous inorganic materials

Evaluating a fractal curve's approximate length by walking a compass defines a compass exponent. Long ago, I showed that for a self-similar curve (e.g., a model of coastline), the compass exponent coincides with all the other forms of the fractal dimension, e.g., the similarity, box or mass dimensions. Now walk a compass along a self-affine curve, such as a scalar Brownian record B(t). It will be shown that a full description in terms of fractal dimension is complex. Each version of dimension has a local and a global value, separated by a crossover. First finding: the basic methods of evaluating the global fractal dimension yield 1: globally, a self-affine fractal behaves as it if were not fractal. Second finding: the box and mass dimensions are 1.5, but the compass dimension is D = 2. More generally, for a fractional Bownian record BH(t), (e.g., a model of vertical cuts of relief), the global fractal dimensions are 1, several local fractal dimensions are 2-H, and the compass dimension is 1/H. This 1/H is the fractal dimension of a self-similar fractal trail, whose definition was already implicit in the definition of the record of BH(t).

http://iopscience.iop.org/article/10.1088/0031-8949/32/4/001/pdf

Self-Affine Fractals and Fractal Dimension

The mechanical and hydraulic behavior of discontinuities in rock, such as joints and faults, depends strongly on the topography of the contacting surfaces and the degree of correlation between them. Understanding this behavior over the scales of interest in the earth requires knowledge of how topography or roughness varies with surface size. Using two surface profilers, each sensitive to a particular scale of topographic features, we have studied the topography of various natural rock surfaces from wavelengths less than 20 microns to nearly 1 meter. The surfaces studied included fresh natural joints (mode I cracks) in both crystalline and sedimentary rocks, a frictional wear surface formed by glaciation, and a bedding plane surface. There is remarkable similarity among these surfaces. Each surface has a “red noise” power spectrum over the entire frequency band studied, with the power falling off on average between 2 and 3 orders of magnitude per decade increase in spatial frequency. This implies a strong increase in rms height with surface size, which has little tendency to level off for wavelengths up to 1 meter. These observations can be interpreted using a fractal model of topography. In this model the scaling of the surface roughness is described by the fractal dimension D. The topography of these natural rock surfaces cannot be described by a single fractal dimension, for this parameter was found to vary significantly with the frequency band considered. This observed inhomogeneity in the scaling parameter implies that extrapolation of roughness to other bands of interest should be done with care. Study of the increase in rms height with profile length for two extreme cases from our data provides an idea of the expected variation in mechanical and hydraulic properties for natural discontinuities in rock. This indicates that in addition to the scaling of topography, the degree of correlation between the contacting surfaces is important to quantify.

Broad bandwidth study of the topography of natural rock surfaces

When a piece of metal is fractured either by tensile or impact loading (pulling or hitting), the fracture surface that is formed is rough and irregular. Its shape is affected by the metal's microstructure (such as grains, inclusions and precipitates, whose characteristic length is large relative to the atomic scale), as well as by ‘macrostructural’ influences (such as the size, the shape of the specimen, and the notch from which the fracture begins). However, repeated observation at various magnifications also reveals a variety of additional structures that fall between the ‘micro’ and the ‘macro’ and have not yet been described satisfactorily in a systematic manner. The experiments reported here reveal the existence of broad and clearly distinct zone of intermediate scales in which the structure is modelled very well by a fractal surface. A new method, slit island analysis, is introduced to estimate the basic quantity called the fractal dimension, D. The estimate is shown to agree with the value obtained by fracture profile analysis, a spectral method. Finally, D is shown to be a measure of toughness in metals.

Fractal character of fracture surfaces of metals

Silicon–oxygen and aluminum–oxygen compounds exhibit significant XPS Auger and photoelectron chemical shifts that are accurately measurable. Chemical state plots of KLL Auger kinetic energy versus 2p photoelectron energy permit identification of chemical species from the locations of their points on the plots. The KLL Auger electrons of Al and Si were generated by the bremsstrahlung component of the radiation, with conventional instrumentation. The location of points on the plots can be understood on the basis of polarizability of the environment (on the Auger parameter grid of lines, slope +1) and on the basis of the factors contributing to the energy of the final state ion in the Auger transition (a grid of line, slope −1). Tetrahedral aluminum has a significantly smaller Auger parameter than octahedral aluminum, and this difference is repeated, but with reduced magnitude on the similar plots for silicon and oxygen lines for the same compounds. Otherwise, the Auger parameters for this class of compounds...

Auger and photoelectron line energy relationships in aluminum–oxygen and silicon–oxygen compounds

Fractal geometry is a non-Euclidean geometry which has been developed to analyze irregular or fractional shapes In this paper, fracture in ceramic materials is analyzed as a fractal process This means that fracture is viewed as a self-similar process We have examined the fracture surfaces of six different alumina materials and five glass-ceramics, with different microstructures, to test for fractal behavior Slit island analysis and Fourier transform methods were used to determine the fractal dimension, D, of successively sectioned fracture surfaces We found a correlation between increasing the fractional part of the fractal dimension and increasing toughness In other words, as the toughness increasing the fracture surface increases in roughness However, more than just a measure of roughness, the applicability of fractal geometry to fracture implies a mechanism for generation of the fracture surface The results presented here imply that brittle fracture is a fractal process; this means that we should be able to determine processes on the atomic scale by observing the macroscopic scale by finding the generator shape and the scheme for generation inherent in the fractal process

Quantitative Analysis of Brittle Fracture Surfaces Using Fractal Geometry

Heat treatments were utilized in 5Ni and 9Ni steel which resulted in the development of tempered microstructures which contained either no measurable retained austenite (<0.5 pct) or approximately 4 to 5 pct retained austenite as determined by X-ray diffraction. Microstructural observations coupled with the results of tensile testing indicated that the formation of retained austenite correlated with a decrease in carbon content of the matrix. Relative values ofKIC at 77 K were estimated from slow bend precracked Charpy data using both the COD and equivalent energy measurements. In addition, Charpy impact properties at 77 K were determined. In the 9Ni alloy, optimum fracture toughness was achieved in specimens which contained retained austenite. This was attributed to changes in yield and work hardening behavior which accompanied the microstructural changes. In the 5Ni alloy, fracture toughness equivalent to that observed in the 9Ni alloy was developed in grain refined and tempered microstructures containing <0.5 pct retained austenite. A decrease in fracture toughness was observed in grain refined 5Ni specimens containing 3.8 pct retained austenite due to the premature onset of unstable cracking. This was attributed to the transformation of retained austenite to brittle martensite during deformation. It was concluded that the formation of thermally stable retained austenite is beneficial to the fracture toughness of Ni steels at 77 K as a result of austenite gettering carbon from the matrix during tempering. However, it was also concluded that the mechanical stability of the retained austenite is critical in achieving a favorable enhancement of cryogenic fracture toughness properties.

The effect of heat treatment on microstructure and cryogenic fracture properties in 5Ni and 9Ni steel

Observations of characteristic markings on the fracture surface of brittle materials can be used to quantitatively describe non-equilibrium fracture. The relationship between quantitative fractography and fracture mechanics is first presented to describe the fracture of primary bonds as a fractal process. Next, molecular dynamics (MD) and molecular orbital (MO) modelling of the fracture in silicon single crystal and silica glass demonstrates that experimentally measurable quantities can be obtained from modelling. The fracture process is then described as a series of quantized, bond reconfiguration events related to the production of free volume at the crack tip. A series of these reconfigurations along the crack front, due to thermal vibrations and lowest energy configurations, develop into the mirror-mist-hackle and crack branching patterns often observed. The fractal dimensional increment, D∗, is described as a scaling factor for both the fracture energy and the geometry of the fracture surfac...

D. E. Passoja

Papers

Fractal character of fracture surfaces of metals

Auger and photoelectron line energy relationships in aluminum–oxygen and silicon–oxygen compounds

Quantitative Analysis of Brittle Fracture Surfaces Using Fractal Geometry

The effect of heat treatment on microstructure and cryogenic fracture properties in 5Ni and 9Ni steel

Fractal dimension as a characterization of free volume created during fracture in brittle materials