Compression Of Cu Research Articles

Experimental and theoretical examination of shock-compressed copper through the fcc to bcc to melt phase transitions

Recent studies show a face-centered cubic (fcc) to body-centered cubic (bcc) transformation along the shock Hugoniot for several metals (i.e., Cu, Au, and Ag). Here, we combine laser-shock compression of Cu foils on nanosecond timescales with in situ x-ray diffraction (XRD) to examine the microstructural changes with stress. We study the fcc phase and the phase transition from fcc to bcc (pressures greater than 180 GPa). Textural analysis of the azimuthal intensities from the XRD images is consistent with transformation into the bcc phase through the Pitsch-distortion mechanism. We use embedded atom model molecular dynamics simulations to determine the stability of the bcc phase in pressure–temperature space. Our results indicate that the bcc phase is stabilized only at high temperatures and remains stable at pressures greater than 500 GPa.

Coupling of a multi-GPU accelerated elasto-visco-plastic fast Fourier transform constitutive model with the implicit finite element method

This paper presents an implementation of the elasto-visco-plastic fast Fourier transform (EVPFFT) crystal plasticity model in the implicit finite element (FE) method of Abaqus standard through a user material (UMAT) subroutine to provide a constitutive relationship between stress and strain at FE integration points. To facilitate the implicit coupling ensuring fast convergence rates, an analytical Jacobian is derived. The constitutive response at every integration point is obtained by the full-field homogenization over an explicit microstructural cell. The implementation is a parallel computing approach involving multi-core central processing units (CPUs) and graphics processing units (GPUs) for computationally efficient simulations of large plastic deformation of metallic components with arbitrary geometry and loading boundary conditions. To this end, the EVPFFT solver takes advantages of GPU acceleration utilizing Nvidia’s high performance computing software development kit (SDK) compiler and compute unified device architecture (CUDA) FFT libraries, while the FE solver leverages the message passing interface (MPI) for parallelism across CPUs. The high-performance hybrid CPU-GPU multi-level framework is referred to as FE-GPU-EVPCUFFT. Simulations of simple compression of Cu and large strain cyclic reversals of dual phase (DP) 590 have been used to benchmark the accuracy of the implementation in predicting the mechanical response and texture evolution. Subsequently, two applications are presented to illustrate the potential and utility of the multi-level simulation strategy: 4-point bending of textured Zr bars, in which the model captures the shape variations as a consequence of texture with respect to the bending plane and another bending of DP1180, in which the model reveals details of spatial micromechanical fields.

New large-strain FFT-based formulation and its application to model strain localization in nano-metallic laminates and other strongly anisotropic crystalline materials

This paper presents a new robust large-strain (LS) elasto-viscoplastic (EVP) formulation based on Fast Fourier Transforms (FFTs) for the prediction of the micro-mechanical response and microstructure evolution of polycrystalline and multiphase materials, with emphasis on the effect of strong crystallographic and/or morphologic anisotropy on localization of plastic deformation. The novel LS-EVPFFT formulation allows treatment of complex initial geometries and large deformations considering three grids of material points: a regular grid in the reference configuration, where FFTs can be performed; an irregular grid in the initial configuration, created by applying a stress-free displacement field to the reference regular grid; and an irregular grid in the current configuration, undergoing large strains and rotations as the material is loaded. Further numerical stability of the new formulation also required the use of a novel expression for the discrete modified Green's operator, which reduces spurious field oscillations. After presenting and validating the new formulation by comparison with pre-existing implementations and analytical solutions, LS-EVPFFT is applied to the prediction of slip and kink bands formation in polycrystalline columnar ice, and kink bands in single crystal zinc wires, showing good agreement with classic experiments. Finally, the model is used to study kink band formation during compression of Cu–Nb nano-metallic laminates (NMLs), in which accurate treatment of the complex geometry associated with the tortuosity of interfaces and large deformations become critical, showing consistency with corresponding micropillar experiments.

Оценка вкладов различных механизмов в сопротивление деформированию монокристаллов сплава Cu–12 ат.% Al

The evolution of the structure in the process of plastic deformation by compression of Cu – 12 at.% Al single crystals is investigated. Data on the stress-strain curve, deformation stages and the relationship of stages with the types of forming substructures are presented. Quantitative measurements of various parameters characterizing the substructures were carried out. The results are presented in the form of a diagram of the dependence of the fraction of substructures on the density of dislocations. Dependences of the distances between non-reactive intersections of dislocations, inter-dislocation reactions, obstacles of different types, and dislocation lines on the degree of strain are shown. Particular attention is paid to the quantitative assessment of the contributions to the flow stress from local obstacles and long-range elastic stress fields, as well as the contributions to strain associated with the development of slip and twinning.

Ab Initio Phase Diagram of Copper

Copper has been considered as a common pressure calibrant and equation of state (EOS) and shock wave (SW) standard, because of the abundance of its highly accurate EOS and SW data, and the assumption that Cu is a simple one-phase material that does not exhibit high pressure (P) or high temperature (T) polymorphism. However, in 2014, Bolesta and Fomin detected another solid phase in molecular dynamics simulations of the shock compression of Cu, and in 2017 published the phase diagram of Cu having two solid phases, the ambient face-centered cubic (fcc) and the high-PT body-centered cubic (bcc) ones. Very recently, bcc-Cu has been detected in SW experiments, and a more sophisticated phase diagram of Cu with the two solid phases was published by Smirnov. In this work, using a suite of ab initio quantum molecular dynamics (QMD) simulations based on the Z methodology, which combines both direct Z method for the simulation of melting curves and inverse Z method for the calculation of solid–solid phase boundaries, we refine the phase diagram of Smirnov. We calculate the melting curves of both fcc-Cu and bcc-Cu and obtain an equation for the fcc-bcc solid–solid phase transition boundary. We also obtain the thermal EOS of Cu, which is in agreement with experimental data and QMD simulations. We argue that, despite being a polymorphic rather than a simple one-phase material, copper remains a reliable pressure calibrant and EOS and SW standard.

Effect of HfO2 Nanoparticles on the Shape and Parameters of Pseudoelastic Stress–Strain Curves of Cu–Al–Ni Alloy Single Crystals

The effect of hafnium dioxide (HfO2) disperse nanoparticles on the shape and parameters of stress–strain curves for the compression of Cu–13.5 wt %Al–4.0 wt %Ni alloy single crystals with memory effect has been investigated. It is found that 30-nm nanoparticles with a volume fraction of 1% affect the shape of pseudoelastic stress–strain curves of an alloy crystal, namely, substantially elevate its (martensite) strain-hardening coefficient θ and deformation work and eliminate deforming stress drops associated with the existence of interfacial stresses under martensite transformation, but do not affect the hysteresis of pseudoelastic stress–strain curves and deformation of shape memory. Simulation of pseudoelastic stress–strain curves and analysis of results using the smeared martensite transformation have revealed that the increase in coefficient θ ~ ω–1 and elimination of stress drops on pseudoelastic stress–strain curves are associated with a considerable (order-of-magnitude) decrease in martensite nucleus volume ω ~ w, where w is the transverse size of nanoparticles.

Влияние наночастиц HfO-=SUB=-2-=/SUB=- на форму и параметры кривых псевдоупругой деформации монокристаллов сплава Cu--Al--Ni

AbstractThe effect of hafnium dioxide (HfO_2) disperse nanoparticles on the shape and parameters of stress–strain curves for the compression of Cu–13.5 wt %Al–4.0 wt %Ni alloy single crystals with memory effect has been investigated. It is found that 30-nm nanoparticles with a volume fraction of 1% affect the shape of pseudoelastic stress–strain curves of an alloy crystal, namely, substantially elevate its (martensite) strain-hardening coefficient θ and deformation work and eliminate deforming stress drops associated with the existence of interfacial stresses under martensite transformation, but do not affect the hysteresis of pseudoelastic stress–strain curves and deformation of shape memory. Simulation of pseudoelastic stress–strain curves and analysis of results using the smeared martensite transformation have revealed that the increase in coefficient θ ~ ω^–1 and elimination of stress drops on pseudoelastic stress–strain curves are associated with a considerable (order-of-magnitude) decrease in martensite nucleus volume ω ~ w , where w is the transverse size of nanoparticles.

Shock compression of Cu x Zr100−x metallic glasses from molecular dynamics simulations

The shock response of Cu x Zr100−x (x = 30, 50 and 70) metallic glasses (MGs) is characterized using large-scale molecular dynamics simulations. A wide range of piston velocities U p = 0.125–2.5 km/s are simulated corresponding to shock pressures from 3 to 130 GPa. Independent of composition, the metallic glasses exhibit the following shock wave propagation regimes: (1) single elastic shock wave for U p < 0.25 km/s, (2) split elastic and plastic shock waves for 0.25 < U p < 0.75 km/s and (3) overdriven plastic shock wave with a narrow elastic precursor for U p > 0.75 km/s. Within the split wave and overdriven regimes, the amplitude of the elastic precursor increases with increasing shock intensity, thereby indicating a pressure-dependent yield criterion. Hugoniot states are strongly dependent on the Cu content of the MG with Cu70Zr30 exhibiting a much higher resistance to plastic deformation than either Cu50Zr50 or Cu30Zr70.

Strain gradients in Cu–Fe thin films and multilayers during micropillar compression

Plastic strain gradients can influence the work-hardening behaviour of metals due to the accumulation of geometrically necessary discolations at the micron/submicron scale. A finite element model based on the conventional theory of mechanism-based strain-gradient plasticity has been developed to simulate the micropillar compression of Cu–Fe thin films and multilayers. The modelling results show that the geometric constraints lead to inhomogeneous deformation in the Cu layers, which agrees well with the bulging of Cu layers observed experimentally. Plastic strain gradients develop inside the individual layers, leading to extra work-hardening due to the accumulation of geometrically necessary dislocations. In the multilayer specimens, the Cu layers deform more severely than the Fe layers, resulting in the development of tensile stresses in the Fe layers. It is proposed that these tensile stresses are responsible for the development of micro-cracks in the Fe layers.

High-pressure, high-strain-rate lattice response of shocked materials

Laser-based shock experiments have been conducted in thin Si and Cu crystals at pressures above the published Hugoniot Elastic Limit (HEL) for these materials. In situ x-ray diffraction has been used to directly measure the response of the shocked lattice during shock loading. Static film and x-ray streak cameras recorded x rays diffracted from lattice planes both parallel and perpendicular to the shock direction. In addition, experiments were conducted using a wide-angle detector to record x rays diffracted from multiple lattice planes simultaneously. These data showed uniaxial compression of Si (100) along the shock direction and three-dimensional compression of Cu (100). In the case of the Si diffraction, there was a multiple wave structure observed. This is evaluated to determine whether there is a phase transition occurring on the time scale of the experiments, or the HEL is much higher than previously reported. Results of the measurements are presented.

Multiple film plane diagnostic for shocked lattice measurements (invited)

Laser-based shock experiments have been conducted in thin Si and Cu crystals at pressures above the Hugoniot elastic limit. In these experiments, static film and x-ray streak cameras recorded x rays diffracted from lattice planes both parallel and perpendicular to the shock direction. These data showed uniaxial compression of Si(100) along the shock direction and three-dimensional compression of Cu(100). In the case of the Si diffraction, there was a multiple wave structure observed, which may be due to a one-dimensional phase transition or a time variation in the shock pressure. A new film-based detector has been developed for these in situ dynamic diffraction experiments. This large-angle detector consists of three film cassettes that are positioned to record x rays diffracted from a shocked crystal anywhere within a full π steradian. It records x rays that are diffracted from multiple lattice planes both parallel and at oblique angles with respect to the shock direction. It is a time-integrating measurement, but time-resolved data may be recorded using a short duration laser pulse to create the diffraction source x rays. This new instrument has been fielded at the OMEGA and Janus lasers to study single-crystal materials shock compressed by direct laser irradiation. In these experiments, a multiple wave structure was observed on many different lattice planes in Si. These data provide information on the structure under compression.

Plastic deformation under compression of Cu–Zn–Al martensitic single crystals

In Cu–Zn–Al single crystals, a bcc to 18R martensitic transition can be induced either termally or under applied stresses. In the latter case, a martensite single crystal is obtained. In this work, the plastic deformation behavior of the 18R martensitic phase for two different compositions ( e/ a=1.43 and e/ a=1.48, M s≈263 K) is analyzed in order to find out possible differences in both the mechanical behavior and the microstructure. Optical microscopy and transmission electron microscopy were used to study surface and bulk defects. The observed primary slip system was the same for all the samples, independently of the composition and orientation: (011)[100] β, which corresponds to slip in the basal plane of the martensite. In addition, for compression axes near [100] β, a secondary slip system appeared. The corresponding surface traces were far larger than those corresponding to the primary slip system. The measured resolved shear stresses to activate the primary slip system were on average 15% lower for compositions with e/ a=1.43, compared to the samples with e/ a=1.48. The results obtained for the yield stress of the martensite lend support to the role of plasticity of this phase on the nucleation and growth of the surface and bulk defects generated after pseudo-elastic cycling.

Effects of anharmonic strain on the phase stability of epitaxial films and superlattices: Applications to noble metals

Epitaxial strain energies of epitaxial films and bulk superlattices are studied via first-principles total energy calculations using the local-density approximation. Anharmonic effects due to large lattice mismatch, beyond the reach of the harmonic elasticity theory, are found to be very important in Cu/Au (lattice mismatch 12%), Cu/Ag (12%) and Ni/Au (15%). We find that <001> is the elastically soft direction for biaxial expansion of Cu and Ni, but it is <201> for large biaxial compression of Cu, Ag, and Au. The stability of superlattices is discussed in terms of the coherency strain and interfacial energies. We find that in phase-separating systems such as Cu-Ag the superlattice formation energies decrease with superlattice period, and the interfacial energy is positive. Superlattices are formed easiest on (001) and hardest on (111) substrates. For ordering systems, such as Cu-Au and Ag-Au, the formation energy of superlattices increases with period, and interfacial energies are negative. These superlattices are formed easiest on (001) or (110) and hardest on (111) substrates. For Ni-Au we find a hybrid behavior: superlattices along <111> and <001> like in phase-separating systems, while for <110> they behave like in ordering systems. Finally, recent experimental results on epitaxial stabilization of disordered Ni-Au and Cu-Ag alloys, immiscible in the bulk form, are explained in terms of destabilization of the phase separated state due to lattice mismatch between the substrate and constituents.