Inelastic Amplitudes Research Articles

Angular Momentum Loss due to Tidal Effects in the Post-Minkowskian Expansion.

We calculate the tidal corrections to the loss of angular momentum in a two-body collision at leading post-Minkowskian order from an amplitude-based approach. The eikonal operator allows us to efficiently combine elastic and inelastic amplitudes, and captures both the contributions due to genuine gravitational-wave emissions and those due to the static gravitational field. We calculate the former by harnessing powerful collider-physics techniques such as reverse unitarity, thereby reducing them to cut two-loop integrals, and cross check the result by performing an independent calculation in the post-Newtonian limit. For the latter, we can employ the results of P. Di Vecchia et al. [Angular momentum of zero-frequency gravitons, J. High Energy Phys. 08 (2022) 172.JHEPFG1029-847910.1007/JHEP08(2022)172], where static-field effects were calculated for generic gravitational scattering events using the leading soft graviton theorem.

One-loop inelastic amplitudes from tree-level elasticity in 2d

We investigate the perturbative integrability of different quantum field theories in 1+1 dimensions at one loop. Starting from massive bosonic Lagrangians with polynomial-like potentials and absence of inelastic processes at the tree level, we derive a formula reproducing one-loop inelastic amplitudes for arbitrary numbers of external legs. We show that any one-loop inelastic amplitude is equal to its tree-level version, in which the masses of particles and propagators are corrected by one-loop bubble diagrams. These amplitudes are nonzero in general and counterterms need to be added to the Lagrangian to restore the integrability at one loop. For the class of simply-laced affine Toda theories, we show that the necessary counterterms are obtained by scaling the potential with an overall multiplicative factor, proving in this way the one-loop integrability of these models. Even though we focus on bosonic theories with polynomial-like interactions, we expect that the on-shell techniques used in this paper to compute amplitudes can be applied to several other models.

Shot noise in resonant tunneling: Role of inelastic scattering

We study the influence of inelastic processes on shot noise and the Fano factor for a one-dimensional double-barrier structure, where resonant tunneling takes place between two terminals. Most studies to date have found, by means of various approximate or phenomenological methods, that shot noise is insensitive to dephasing caused by inelastic scattering. In this paper, we explore the status of this statement by deriving a general Landaur-B\"uttiker-type formula that expresses the current noise and Fano factor in a one-dimensional conductor through inelastic scattering amplitudes. For a double-barrier structure, exact scattering amplitudes are calculated in the presence of a time-dependent potential. As an example of dephasing potential, we consider the one induced by equilibrium phonons. We calculate transmission coefficients of a double-barrier structure for these two types of phonon-induced dephasing. In the case of diffusive phase relaxation valid for one dimension phonons, the resonant level has a Lorentzian shape. For phonons whith high dimensions logarithmic dephasing realized which leads to an unusual shape of the size-quantized level characterized by the two energy scales. We further calculate the Fano factor for these types of dephasing, using exact expressions for inelastic transmission and reflection amplitudes. It turned out that when an integer number of levels fall into the energy window of width eV, where V is the voltage applied to the structure, the Fano factor is really insensitive to inelastic processes inside the structure and coincides with the prediction of phenomenological models with an accuracy of small corrections depending on these processes. On the contrary, at low voltages, when the eV window is smaller than the level width, this dependence is particularly pronounced and the phenomenological formula does not work.

Tree level integrability in 2d quantum field theories and affine Toda models

We investigate the perturbative integrability of massive (1+1)-dimensional bosonic quantum field theories, focusing on the conditions for them to have a purely elastic S-matrix, with no particle production and diagonal scattering, at tree level. For theories satisfying what we call ‘simply-laced scattering conditions’, by which we mean that poles in inelastic 2 to 2 processes cancel in pairs, and poles in allowed processes are only due to one on-shell propagating particle at a time, the requirement that all inelastic amplitudes must vanish is shown to imply the so-called area rule, connecting the 3-point couplings {C}_{abc}^{(3)} to the masses ma, mb, mc of the coupled particles in a universal way. We prove that the constraints we find are universally satisfied by all affine Toda theories, connecting pole cancellations in amplitudes to properties of the underlying root systems, and develop a number of tools that we expect will be relevant for the study of loop amplitudes.

The eikonal approach to gravitational scattering and radiation at mathcal{O} (G3)

Using mathcal{N} = 8 supergravity as a theoretical laboratory, we extract the 3PM gravitational eikonal for two colliding massive scalars from the classical limit of the corresponding elastic two-loop amplitude. We employ the eikonal phase to obtain the physical deflection angle and to show how its non-relativistic (NR) and ultra-relativistic (UR) regimes are smoothly connected. Such a smooth interpolation rests on keeping contributions to the loop integrals originating from the full soft region, rather than restricting it to its potential sub-region. This task is efficiently carried out by using the method of differential equations with complete near-static boundary conditions. In contrast to the potential-region result, the physical deflection angle includes radiation-reaction contributions that are essential for recovering the finite and universal UR limit implied by general analyticity and crossing arguments. We finally discuss the real emission of massless states, which accounts for the imaginary part of the 3PM eikonal and for the dissipation of energy-momentum. Adopting a direct approach based on unitarity and on the classical limit of the inelastic tree-level amplitude, we are able to treat mathcal{N} = 8 and General Relativity on the same footing, and to complete the conservative 3PM eikonal in Einstein’s gravity by the addition of the radiation-reaction contribution. We also show how this approach can be used to compute waveforms, as well as the differential and integrated spectra, for the different radiated massless fields.

Effect of Stress Gradient on Heat Cycle Fatigue Life Prediction of Solder Joints by Repetitive Bending Test

Strength of solder joints is usually evaluated by a shear test and a pull test. The reliability of the solder joint is evaluated by the repetitive pull tests of solder bulk specimens. However, the stress and strain field that caused by thermal load on the solder joint of the product model for estimating the reliability is different from these tests. Therefore, we proposed a repetitive bending test as a reliability test of solder joints producing the stress and strain field caused at the solder joint of product model. We proposed a repetitive multi-point bending test as a method to predict the fatigue life of the solder joint in the thermal cycle test in a short period of time. The influence of strain gradient on the inelastic strain amplitude used for lifetime evaluation is estimated. The controllability of the strain gradient by the three-point bending test parameters is investigated. The effect of residual stress on inelastic strain amplitude during sample preparation for thermal cycle test is also evaluated.

Universality of ultra-relativistic gravitational scattering

We discuss the ultra-relativistic gravitational scattering of two massive particles at two-loop (3PM) level. We find that in this limit the real part of the eikonal, determining the deflection angle, is universal for gravitational theories in the two derivative approximation. This means that, regardless of the number of supersymmetries or the nature of the probes, the result connects smoothly with the massless case discussed since the late eighties by Amati, Ciafaloni and Veneziano. We analyse the problem both by using the analyticity and crossing properties of the scattering amplitudes and, in the case of the maximally supersymmetric theory, by explicit evaluation of the 4-point 2-loop amplitude using the results for the integrals in the full soft region. The first approach shows that the observable we are interested in is determined by the inelastic tree-level amplitude describing the emission of a graviton in the high-energy double-Regge limit, which is the origin of the universality property mentioned above. The second approach strongly suggests that the inclusion of the whole soft region is a necessary (and possibly sufficient) ingredient for recovering ultra relativistic finiteness and universality at the 3PM level. We conjecture that this universality persists at all orders in the PM expansion.

Simulation of Cyclic Loading on Pipe Elbows Using Advanced Plane-Stress Elastoplasticity Models1

Abstract This work investigates the response of industrial steel pipe elbows subjected to severe cyclic loading (e.g., seismic or shutdown/startup conditions), associated with the development of significant inelastic strain amplitudes of alternate sign, which may lead to low-cycle fatigue. To model this response, three cyclic-plasticity hardening models are employed for the numerical analysis of large-scale experiments on elbows reported elsewhere. The constitutive relations of the material model follow the context of von Mises cyclic elasto-plasticity, and the hardening models are implemented in a user subroutine, developed by the authors, which employs a robust numerical integration scheme, and is inserted in a general-purpose finite element software. The three hardening models are evaluated in terms of their ability to predict the strain range at critical locations, and in particular, strain accumulation over the load cycles, a phenomenon called “ratcheting.” The overall good comparison between numerical and experimental results demonstrates that the proposed numerical methodology can be used for simulating accurately the mechanical response of pipe elbows under severe inelastic repeated loading. Finally, this paper highlights some limitations of conventional hardening rules in simulating multi-axial material ratcheting.

Low cycle fatigue life modelling using finite element strain range partitioning for a steam turbine rotor steel

Materials made for modern steam power plants are required to withstand high temperatures and flexible operational schedule. Mainly to achieve high efficiency and longer components life. Nevertheless, materials under such conditions experience crack initiations and propagations. Thus, life prediction must be made using accurate fatigue models to allow flexible operation. In this study, fully reversed isothermal low cycle fatigue tests were performed on a turbine rotor steel called FB2. The tests were done under strain control with different total strain ranges and temperatures (20 °C to 625 °C). Some tests included dwell time to calibrate the short-time creep behaviour of the material. Different fatigue life models were evaluated based on total life approach. The stress-based fatigue life model was found unusable at 600 °C, while the strain-based models in terms of total strain or inelastic strain amplitudes displayed inconsistent behaviour at 500 °C. To construct better life prediction, the inelastic strain amplitudes were separated into plastic and creep components by modelling the deformation behaviour of the material, including creep. Based on strain range partitioning approach, the fatigue life depends on different damage mechanisms at different strain ranges at 500 °C. This allows for the formulation of life curves based on either plasticity-dominated damage or creep-dominated damage. At 600 °C, creep dominated while at 500 °C creep only dominates for higher strain ranges. The deformation mechanisms at different temperatures and total strain ranges were characterised by scanning electron microscopy and by quantifying the amount of low angle grain boundaries. The quantification of low angle grain boundaries was done by electron backscatter diffraction. Microscopy revealed that specimens subjected to 600 °C showed signs of creep damage in the form of voids close to the fracture surface. In addition, the amount of low angle grain boundaries seems to decrease with the increase in temperature even though the inelastic strain amplitude was increased. The study indicates that a significant amount of the inelastic strain comes from creep strain as opposed of being all plastic strain, which need to be taken into consideration when constructing a life prediction model.

Low cycle fatigue modelling of a steam turbine rotor steel

Materials in steam turbine rotors are subjected to cyclic loads at high temperature, causing cracks to initiate and grow. To allow for more flexible operation, accurate fatigue models for life prediction must not be overly conservative. In this study, fully reversed low cycle fatigue tests were performed on a turbine rotor steel called FB2. The tests were done isothermally, within temperature range of room temperature to 600 °C, under strain control with 0.8-1.2 % total strain range. Some tests included hold time to calibrate the short-time creep behaviour of the material. Different fatigue life models were constructed. The life curve in terms of stress amplitude was found unusable at 600 °C, while the life curve in terms of total strain or inelastic strain amplitudes displayed inconsistent behaviour at 500 °C. To construct better life model, the inelastic strain amplitudes were separated into plastic and creep components by modelling the deformation behaviour of the material, including creep. Based on strain range partitioning approach, the fatigue life depends on different damage mechanisms at different strain ranges. This allowed the formulation of life curves based on plasticity or creep domination, which showed creep domination at 600 °C, while at 500 °C, creep only dominates for higher strain range.

A closed-form analytical solution for the ratcheting response of steel tubes with wall-thinning under inelastic symmetric constant amplitude cyclic bending

Metallic tubes experiences a progressive accumulation of ovalisation, or ratchet, under cyclic inelastic bending. During their life time, the tubes may also suffer from different types of mechanically and/or chemically originated defects. The current paper discusses a closed-form solution for the response analysis of defective circular steel tubes under monotonic and cyclic inelastic bending. The defect in the tube is idealised as a uniform patch type wall thinning.The material model considers the cyclic hardening/softening features based on a combined non-linear hardening law. To account for the non-fading memory characteristics of the steel material, the hardening modulus in each half-cycle is introduced as a state variable. A modified version of the Bailey–Norton law is used for the cyclic growth (cyclic creep) in the ovalisation of the cross-section. In overall, the solution considers the geometrical non-linearity due to the ovalisation as well as the hysteresis effects.The study also includes monotonic and cyclic inelastic bending experiments on small-scale, thick-walled, high strength, low alloy carbon steel defective tubes. The analytical solutions for the inelastic monotonic and cyclic bending of the tubes are validated against these experimental data and reasonable agreements are noticed and reported.

Resonant Inelastic X-ray Scattering Amplitudes and Cross Sections in the Algebraic Diagrammatic Construction/Intermediate State Representation (ADC/ISR) Approach.

A scheme has been derived and implemented to gain computational access to the full electronic part of the Kramers-Heisenberg-Dirac (KHD) expression for resonant and nonresonant inelastic scattering amplitudes. Our implementation of this scheme is based on the complex polarization propagator in the algebraic diagrammatic construction (ADC) framework and within its intermediate state representation (ISR). The hierarchy of the second- and third-order ADC/ISR computational schemes known as ADC(2), ADC(2)-x, and ADC(3/2) is considered, and the calculated resonant inelastic X-ray scattering (RIXS) amplitudes and transition strengths for water are in excellent agreement with recent experimental data.

Mechanical response and dislocation substructure of a cast austenitic steel under low cycle fatigue at elevated temperatures

With the increase of exhaust temperature in automobiles resulting from the stricter environmental and fuel consumption regulations, high temperature fatigue failure of exhaust manifolds is being a significant issue for safety concern. In this research, low cycle fatigue behavior of a Nb-bearing cast austenitic steel with the "Chinese-script" type primary Nb(C,N), was investigated in the temperature range of 600–950°C. It is indicated that the fatigue lifetime was predominantly dependent on the inelastic strain amplitude, in spite of fatigue temperature. However, the change of deformation substructure from dislocation cells, slip bands to subgrains was observed from 600°C to 950°C, which was induced by the increased thermal recovery. Correspondingly, the cyclic stress amplitude changed from cyclic hardening at 600°C to cyclic softening and cyclic stress saturation at 800°C and 950°C, respectively. Besides, strain heterogeneity was also noted between the dendrite core and the interdendritic region, thus regarded as a promotion for crack initiation. The generated data and the understanding will be helpful for alloy design and fatigue lifetime prediction next.

Parameters influencing thermomechanical fatigue of a directionally-solidified Ni-base superalloy

Thermomechanical fatigue (TMF) is a low cycle fatigue process in which material life is correlated to the mechanical strain amplitude. However, it is well known that several other factors influence this life. This paper examines several of these parameters and their influence on life using experiments conducted on a second generation directionally-solidified (DS) Ni-base superalloy. The parameters considered include the influence of the temperature extremums (Tmax of either 750 or 950°C and Tmin of either 100 or 500°C), strain ratio (R∊), the strain-temperature phasing (in-phase (IP) and out-of-phase (OP)), the influence of dwells at the high temperature end of the cycle resulting in a creep–fatigue (CF) interaction, and material anisotropy associated with the grain growth direction (longitudinal versus transverse). Results suggest that the phasing has a primary role in controlling the mechanism of degradation. IP TMF is dominated by crack formation in volumes surrounding debonded carbides for both continuously cycling (CC) and CF at 950 and 750°C, while OP TMF is dominated by surface oxidation and repetitive cracking of the oxide that reforms at the crack tip at 950°C. Decreasing the Tmax to 750°C the environmental and creep effects are reduced resulting in virtually pure fatigue exposure under OP conditions. With decreasing Tmin from 500°C to 100°C was observed an increase in inelastic strain amplitude and corresponding decrease in life. Variations in R∊ were found to have no significant influence on life or stabilized stress behavior. TMF loading in the transverse orientation resulted in life reductions over the longitudinal orientation due to cracks propagating in a transgranular manner. Lastly, only in material exposed to CF with a Tmax of 950°C rafting of the γ′ precipitates was observed.

Fatigue Damage of Al/SiC Composites - Macroscopic and Microscopic Analysis

Abstract The results of comparative examinations of mechanical behaviour during fatigue loads and microstructure assessment before and after fatigue tests were presented. Composites of aluminium matrix and SiC reinforcement manufactured using the KoBo method were investigated. The combinations of two kinds of fatigue damage mechanisms were observed. The first one governed by cyclic plasticity and related to inelastic strain amplitude changes and the second one expressed in a form of ratcheting based on changes in mean inelastic strain. The higher SiC content the less influence of the fatigue damage mechanisms on material behaviour was observed. Attempts have been made to evaluate an appropriate fatigue damage parameter. However, it still needs further improvements.

Durability of a Stress Concentrator-Containing Cantilever Beam Under Cyclic Loading in Bending

The procedure and results of studies on the durability of the cantilever beam metal over the stress concentrator area in pulsed cyclic bending are presented. Comparison of experimental and numerical simulation data resulted in establishing the relation between the durability and cyclic inelastic strain amplitude. The effect of strain hardening and plastic strains on durability was elucidated.

X-ray Thomson scattering as a temperature probe for Gbar shock experiments

In X-ray Thomson scattering (XRTS), spectrally-resolved spectrometry of probe x-rays scattered from matter gives an elastic (ionic) and an inelastic (electronic) feature, whose location, width, and amplitude can be analyzed for electron density and temperature. This diagnostic is complementary to traditional, mechanical EOS measurements which do not directly constrain temperature. XRTS has been demonstrated on planar dynamic-loading experiments at the Omega laser, and a spectrometer has been constructed for use at the National Ignition Facility (NIF). We plan to obtain XRTS measurements into the Gbar regime using hohlraum-driven converging shocks at NIF. In these experiments, the radial profile through the sample at any instant of time varies greatly, though the XRTS signal is dominated by the densest region, which is close to the shock front where simultaneous radiography obtains an EOS measurement.

J0410405 室温で得たSACはんだのクリープひずみと疲労寿命の関係の高温域への適用性([J041-04]工業材料の変形特性・強度およびそのモデル化 損傷・疲労・破壊,機械材料・材料加工部門)

The fatigue life of solder alloys for the slow-fast cyclic loading condition is much shorter than that for the fast-slow cyclic loading condition, despite the two loading conditions having almost equal inelastic strain amplitudes. This suggests that the inelastic strain amplitude is not the best parameter used for evaluating the fatigue life which shows the strain rate dependency. In the previous study, we conducted the fatigue tests using the Sn-3.0Ag-0.5Cu (SAC) solder at RT. The tests employed the cyclic tension-compression loading using the stepped ramp wave (SW) to analyze the stress-creep strain relations during the tests. The analysis result showed that the creep strain amplitude obtained from the stress-creep strain relation had a higher correlation with the fatigue life than the inelastic strain amplitude. In addition, the equation indicating the relationship between the creep strain amplitude and the fatigue life at RT was likely to be useful to predict the fatigue lives at the other temperature. In this study, we investigated the relationships between the creep strain amplitude and the fatigue life for the SAC solder at 343 K and 393 K by conducting the fatigue tests with cyclic tension-compression loading using the SW. Then we attempted to describe the investigated relations at these two temperatures by the above-mentioned equation. As a result, the equation almost expressed the relationships between the creep strain and the fatigue life at 343 K and 393K even though it had been derived from the test results at RT.

Generalized bootstrap equations and possible implications for the NLO odderon

We formulate and discuss generalized bootstrap equations in nonabelian gauge theories. They are shown to hold in the leading logarithmic approximation. Since their validity is related to the self-consistency of the Steinmann relations for inelastic production amplitudes they can be expected to be valid also in NLO. Specializing to the N=4 SYM, we show that the validity in NLO of these generalized bootstrap equations allows to find the NLO Odderon solution with intercept exactly at one, a result which is valid also for the planar limit of QCD.

Color-kinematics duality and the Regge limit of inelastic amplitudes

We investigate tree-level five-point amplitudes in scalar-QCD expressed in terms of Sudakov variables and find the equivalent "gravitational" counterparts using the color-kinematics duality proposed by Bern, Carrasco, and Johannson. Taking the multi-Regge limit in the gravitational amplitudes, we show that those pieces in the coupling of two reggeized gravitons to one on-shell graviton directly stemming from the double copy of the vertex for two reggeized gluons to one on-shell gluon are universal and properly reproduced by the duality.