Finding an accurate stress-strain relation, able to describe the mechanical behavior of metals during {forming} and machining processes, is an important challenge in several fields of mechanics, with significant repercussions in the technological field. Indeed, in order to predict the real mechanical behavior of materials, constitutive laws must be able to take into account elastic, viscous and plastic phenomena. Most constitutive models are based on empirical evidence and/or theoretical approaches, and provide a good prediction of the mechanical behavior of several materials.
Here we present a non linear stress-strain relation based on fractional operators. The proposed constitutive law is based on integral formulation, and takes into account the viscoelastic behavior of the material and the inelastic phenomenon that appears when the stress reaches a particular yielding value. A specific case of the proposed constitutive law for imposed strain history is used to fit experimental data obtained from tensile tests on two kind of metal alloys. A best-fitting procedure demonstrates the accuracy of the proposed stress-strain relation and its results are compared to those obtained with some classical models. We conclude that the proposed model provides the best results in predicting the mechanical behavior for low and high values of stress/strain.
Martensitic transformation induced by cooling NiTi wire under various tensile stresses: martensite variant microstructure, textures, recoverable strains and plastic strains
Materials under complex loading develop large strains and often transition via an elastic instability, as observed in both simple and complex systems. Here, we present Si I under large strain in terms of Lagrangian strain by an $5^{th}$-order elastic potential found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress-Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including elastic instability driving Si I$\rightarrow$II phase transformation (PT) and the shear instabilities. PT conditions for Si I$…
Surface stress, also known as surface tension, is a fundamental material property of any interface. However, measurements of solid surface stress in traditional engineering materials, such as metals and oxides, have proven to be very challenging. Consequently, our understanding relies heavily on untested theories, especially regarding the strain dependence of this property. Here, we take advantage of the high compliance and large elastic deformability of a soft polymer gel to directly measure solid surface stress as a function of strain. As anticipated by theoretical work for metals, we find t…
Stress induced martensitic transformation in NiTi at elevated temperatures: martensite variant microstructures, recoverable strains and plastic strains
Using the notion of eigenstrain produced by the defects formed in a material exposed to high energy neutron irradiation, we develop a method for computing macroscopic elastic stress and strain arising in components of a fusion power plant during operation. In a microstructurally isotropic material, the primary cause of macroscopic elastic stress and strain fields is the spatial variation of neutron exposure. We show that under traction-free boundary conditions, the volume-average elastic stress always vanishes, signifying the formation of a spatially heterogeneous stress state, combining compr…
Strain engineering has attracted great attention, particularly for epitaxial films grown on a different substrate. Residual strains of SiC have been widely employed to form ultra-high frequency and high Q factor resonators. However, to date the highest residual strain of SiC was reported to be limited to approximately 0.6%. Large strains induced into SiC could lead to several interesting physical phenomena, as well as significant improvement of resonant frequencies. We report an unprecedented nano strain-amplifier structure with an ultra-high residual strain up to 8% utilizing the natural resi…
Stress-strain plots based on nanoindentation load-depth curves reflected cracking phenomenon. A transition from ductile to brittle fracture was observed on increasing the depth or load of indenter penetration. A new approach with shape factors in the fracture studies based on radial crack branching and micro-cracking was done. Hardness and modulus plots were fitted with polynomials. The coefficients were varied to obtain different hardness and modulus responses.
The accumulation of residual stress during welding and additive manufacturing is an important effect that can significantly anticipate the workpiece failure. In this work we exploit the physical and analytical transparency of a 1.5D model to show that the deposition of thermally expanded material onto an elastic substrate leads to the accumulation of strain incompatibility. This field, which is the source of residual stress in the system, introduces memory of the construction history even in the absence of plastic deformations. The model is then applied to describe the onset and the progressio…
Metallic glasses deform elastically under stress. However, the atomic-level origin of elastic properties of metallic glasses remain unclear. In this paper using {\em ab initio} molecular dynamics simulations of the Cu$_{50}$Zr$_{50}$ metallic glass under shear strain, we show that the heterogeneous stress relaxation results in the increased charge transfer from Zr to Cu atoms, enhancing the softening of the shear modulus. Changes in compositional short-range order and atomic position shifts due to the non-affine deformation are discussed. It is shown that the Zr subsystem exhibits a stiff beha…
Metallic glasses are known to have a remarkably robust yield strength, admitting Weibull moduli as high as for crystalline engineering alloys. However, their post-yielding behavior is strongly varying, with large scatter in both flow stress levels and strains at failure. Using x-ray tomography we reveal for the first time how a strain-dependent internal evolution of shear-band cavities underlies this unpredictable post yielding response. We demonstrate how macroscopic strain-softening coincides with the first detection of internal shear-band cavitation. Cavity growth during plastic flow is fou…
Increased demands for high-performance materials have led to advanced composite materials with complex hierarchical designs. However, designing a tailored material microstructure with targeted properties and performance is extremely challenging due to the innumerable design combinations and prohibitive computational costs for physics-based solvers. In this study, we employ a neural operator-based framework, namely Fourier neural operator (FNO) to learn the mechanical response of 2D composites. We show that the FNO exhibits high-fidelity predictions of the complete stress and strain tensor fiel…
The stress-strain curves of most metallic alloys are often described using the relatively simple Ramberg-Osgood relationship. Whilst this description captures the overall stress-strain curve under monotonic tensile loading with reasonable overall accuracy, it often presents significant errors in the immediate post-yield region where the interplay between the elastic and plastic strains is particularly significant. This study proposes and develops a new approach to the description of the tensile stress-strain curve based on the Yield Volume Fraction (YVF) function. The YVF description provides …
Various phenomena (phase transformations, chemical reactions, and friction) under high pressures in diamond anvil cell are strongly affected by fields of all components of stress and plastic strain tensors. However, they could not be measured. Even measured pressure distribution contains significant error. Here, we suggest coupled experimental-analytical-computational approaches utilizing synchrotron X-ray diffraction, to solve an inverse problem and find all these fields and friction rules before, during, and after $α$-$ω$ phase transformation in strongly plastically predeformed Zr. Due to ad…
Scale-free phase-field approach (PFA) at large strains and corresponding finite element method (FEM) simulations for multivariant martensitic phase transformation (PT) from cubic Si I to tetragonal Si II in a polycrystalline aggregate are presented. Important features of the model are large and very anisotropic transformation strain tensor $\varepsilon_{t}=\{0.1753;0.1753; -0.447\}$ and stress-tensor dependent athermal dissipative threshold for PT, which produce essential challenges for computations. 3D polycrystals with 55 and 910 stochastically oriented grains are subjected to uniaxial strai…
Strain engineering provides an effective way of tailoring the electronic and optoelectronic properties of semiconductor nanomaterials and nanodevices, giving rise to novel functionalities. Here, we present direct experimental evidence of strain-induced modifications of hole mobility in individual GaAs nanowires, using in situ transmission electron microscopy (TEM). The conductivity of the nanowires varied with applied uniaxial tensile stress, showing an initial decrease of ~5-20% up to a stress of 1~ 2 GPa, subsequently increasing up to the elastic limit of the nanowires. This is attributed to…
The elastocaloric (eC) effects of natural rubber (NR) and shape memory alloys (SMAs) are compared and potential improvement for eC performances of SMAs is proposed. Both the plateau and hysteresis of stress-strain curve in NR and SMAs are observed. They are attributed to the similar phase transformation: strain-induced crystallization (SIC) in NR and martensitic transformation in SMAs. For NR, the drawback of large strain can be reduced by pre-strain. For SMAs, the stress change with strain is smaller in stress plateau regime. Thus, the drawback of large dynamic stress of SMAs is proposed to b…
Background: The determination of yield stress curves for ductile metals from uniaxial material tests is complicated by the presence of tri-axial stress states due to necking. A need exists for a straightforward solution to this problem. Objective: This work presents a simple solution for this problem specific to axis-symmetric specimens. Equivalent uniaxial true strain and true stress, corrected for triaxiality effects, are calculated without resorting to inverse analysis methods. Methods: A computer program is presented which takes shadow images from tensile tests, obtained in a backlight con…
Mechanical properties of graphene prepared by chemical vapor deposition (CVD) are not easily comparable to the properties of nearly perfect graphene prepared by mechanical cleavage. In this work, we attempt to investigate the mechanical performance of CVD graphene (simply supported or embedded in polymer matrix), transferred by two different techniques, under uniaxial loading with simultaneous in-situ monitoring by Raman microspectroscopy. The level of charge transfer doping and strain is assessed using the vector analysis modified for uniaxial strain. The strain distribution across the sample…
The influence on macroscopic work hardening of small, spherical, elastic particles dispersed within a matrix is studied using an isotropic strain gradient plasticity framework. An analytical solution, based on a recently developed yield strength model is proposed. The model accounts for random variations in particle size and elastic properties, and is numerically validated against FE solutions in 2D/3D material cell models. Excellent agreement is found as long as the typical particle radius is much smaller than the material length scale, given that the particle volume fraction is not too large…
The purpose of the present article is to make a model using analytical equations, based on elasticity theory of continuous media for small deformations, with the aim of completely characterizing the material in their mechanical properties as well as the principal stresses-strains of thin films. The approach differs from the standard literature which usually brings crystal symmetries or is directly concerned with crystalline materials. It is entirely possible to define and to analyze anisotropy in elastic media from first principles in thin films. Therefore, the constitutive relation between st…
We demonstrate a method to induce tensile and compressive strain into two-dimensional transition metal dichalcogenide (TMDC) MoS$_{2}$ via the deposition of stressed thin films to encapsulate exfoliated flakes. With this technique we can directly engineer MoS$_{2}$ strain magnitude by changing deposited thin film stress, therefore allowing variable strain to be applied on a flake-to-flake level. These thin film stressors are analogous to SiN$_{x}$ based stressors implemented in industrial CMOS processes to enhance Si mobility, suggesting that our concept is highly scalable and may be applied f…
Inhomogeneous strain may develop in hybrid organic metal-halide perovskite thin films due to thermal expansion mismatch with a fabrication substrate, polycrystallinity or even light soaking. Measuring these spatially varying strains is difficult but of prime importance for understanding the effects on carrier mobility, non-radiative recombination, degradation and other optoelectronic properties. Local strain can be mapped using the shifts in vibrational frequencies using Raman or infrared microscopy. We use density functional theory to investigate the effect of uniaxial strain on the vibration…
The strain-stress relationships for coherent in-plane strain in heterostructures with monoclinic crystal systems: $β$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$ on $(h0l)$ $β$-Ga$_2$O$_3$ as example
A methodology is presented here for deriving true experimental axial stress-strain curves in both tension and compression for monolayer graphene through the shift of the 2D Raman peak that is present in all graphitic materials. The principle behind this approach is the observation that the shift of the 2D wavenumber as a function of strain for different types of PAN based fibres is a linear function of their Young's moduli and, hence, the corresponding value of the shift of the 2D Raman peak over axial stress is, in fact, a constant. By moving across the length scales we show that this value i…
Structural strain severely impacts material properties such as the linear and non-linear optical response. Moreover, strain plays a key role, e.g., in the physics of ferroelectrics and in particular of their domain walls. $μ$-Raman spectroscopy is a well-suited technique for the investigation of such strain effects, as it allows to measure the lattice dynamics locally. However, quantifying and reconstructing strain fields from Raman maps requires knowledge on the strain dependence of phonon frequencies. In this work, we have analyzed both theoretically and experimentally the phonon frequencies…
We have carried out plastic deformation experiments on single-phase samples of the body centered ZrNbTiVHf high-entropy alloy between room temperature and 1150 K. The experiments were carried out on polycrystalline samples with two different grain sizes, in compression at a true constant strain rate of 10-4 1/s. Incremental tests such as stress-relaxation tests, strain-rate changes and temperature changes were carried out in order to determine thermodynamic activation parameters of the plastic deformation process. The material displays a yield-stress anomaly in the temperature range between ab…
Germanium is a strong candidate as a laser source for silicon photonics. It is widely accepted that the band structure of germanium can be altered by tensile strain so as to reduce the energy difference between its direct and indirect band gaps. However, the conventional deformation potential model most widely adopted to describe this transformation happens to have been investigated only up to 1 % uniaxially loaded strains. In this work, we use a micro-bridge geometry to uniaxially stress germanium along [100] up to $\varepsilon_{100}$=3.3 % longitudinal strain and then perform electro-absorpt…
Finite element analysis of stress about a blunt crack tip, emphasizing finite strain and phenomenological and mechanism-based strain gradient plasticity (SGP) formulations, is integrated with electrochemical assessment of occluded-crack tip hydrogen (H) solubility and two H-decohesion models to predict hydrogen environment assisted crack growth properties. SGP elevates crack tip geometrically necessary dislocation density and flow stress, with enhancement declining with increasing alloy strength. Elevated hydrostatic stress promotes high-trapped H concentration for crack tip damage; it is impe…
Nanoindentation is a widely used method for sensitive exploration of the mechanical properties of micromechanical systems. We derived an empirical analysis technique to extract stress-strain field gradient and divergence representations from nanoindentation measurements. With this approach local gradients and heterogeneities can be discovered to obtain more detail about the sample's microstructure, thus enhancing the analytic capacity of the nanoindentation technique. We analysed nanoindentation tests of bulk solid substrates, namely bearing and tooling steel, and fused silica. Oscillations of…
A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed equations that assume pure plastic behavior without elasticity. A method to numerically solve these equations is also presented. In addition to force balance, the equations are derived from the elastic-plastic decomposition of the deformation gradient, the assumption of isotropy, and the assumption that the function mapping the elastic strain to stress is kno…
The measurement of the Si lattice parameter by x-ray interferometry assumes the use of strain-free crystals, which might not be true because of intrinsic stresses due to surface relaxation, reconstruction, and oxidation. We used x-ray phase-contrast topography to investigate the strain sensitivity to the finishing, annealing, and coating of the interferometer crystals.We assessed the topography capabilities by measuring the lattice strain due to films of copper deposited on the interferometer mirror-crystal. A byproduct has been the measurement of the surface stresses after complete relaxation…
From Deposition Stress to Surface Reactivity: Strain-Dependent Hydrogen Evolution on Sputtered Platinum Thin Films
Ruhr-University Bochum（波鸿鲁尔大学）；University Duisburg-Essen（杜伊斯堡-埃森大学）；Center for Interface-Dominated High Performance Materials, (ZGH) Ruhr-University Bochum（波鸿鲁尔大学界面主导高性能材料中心）；University of Copenhagen（哥本哈根大学）
In this paper, we did a systematic comparative study on the accuracy of two computational methods of elastic constants combined with the density functional theory (DFT), the stress-strain method and the energy-strain method. We took metal Ru as a prototype to compare its high-pressure elastic constants calculated by our present stress-strain method with the previous energy-strain results by others. Although the two methods yielded almost the same accuracy of high-pressure elastic constants for Ru, our stress-strain method directly based on the Hooke's law of elasticity theory is much straightf…
