The effect of residual stresses on hardness measurements

The RockwellC hardness,RC, was measured as a function of position on steel rings with different residual-stress profiles through the thickness. An experimental correlation between residual stress andRC was obtained. A relationship between the average pressurep of a spherical indenter, the yield strengthS _y and the residual stress of the material was conceived and used in fitting the experimental data. In order to model the effects of residual stresses on the measured hardness, the von Mises-Hencky (power) yield criterion was utilized, together with an adaptation for residual stresses of the expression for the stress state under a spherical indenter, given in Shaw, Hoshi and Henry. A parameter α was introduced in our calculations to account for the effect of the nonperpendicularity of the residual stresses to the pressurep of the spherical indenter. The proposed model in large measure fits experimental hardness versus residual stress data, and results are consistent with different samples. This model can be used as a basis for the measurement of residual stresses in steel or other materials.     

Spallation of polycarbonate under laser-driven shocks

Laser driven shocks have been used to investigate dynamic failure (spallation) of polycarbonate under uniaxial tensile loading at very high strain rate, of the order of 10 s. First, uninstrumented recovery shots have been performed, post-test examination of the fracture damage has been carried out, and the influences of the experimental parameters (loading conditions and target thickness) have been analyzed. Then, an attempt to model the response of polycarbonate to plane shock loading has been made. On one hand, in-situ measurements have been performed in polycarbonate samples submitted to the plane detonation wave of a strong explosive, and the results have led to content with simple constitutive relations. On the other hand, piezoelectric measurements under laser shocks have provided a characterization of the loading pressure pulse, and comparisons of the measured and computed signals have confirmed the ability of the model to describe wave propagation in polycarbonate. Finally, the spallation experiments have been simulated. A spall strength has been estimated, on the basis of the experimental data, and the predictive capability of the model has been tested. Received: 18 February 1997 / Accepted 1 April 1997     

Experimental study of the shock response of an HMX-based explosive

Experiments have been fired in which the HMX-based explosive EDC37 was subjected to one-dimensional shocks generated by plate impact. The response of the explosive to sustained shocks, double shocks and a short-pulse shock was monitored using embedded particle velocity gauges and shock tracker gauges. The final stages of the growth to detonation process were similar for all of the different input profiles. A strong reactive wave grows and accelerates to overtake and dominate the initial shock. It is shown that the curves showing the growth of the shock and the reactive wave in the sustained shock experiments can be normalised to give universal curves. These curves provides a reference against which to compare the explosive's response, not only to single sustained shocks, but also to double shock and short-pulse inputs. The treatment provides an empirical route for predicting the effects of sustained and more complex shocks on EDC37. PACS 47.40.-x; 82.33.Vx     

Stability of Semi-Discrete Shock Profiles by Means of an Evans Function in Infinite Dimensions

Semi-discrete shock profiles are traveling wave solutions of hyperbolic systems of conservation laws under discretization in space. The existence of semi-discrete shocks has been investigated in earlier papers. Here the spectral stability of those nonlinear waves is addressed, and formulated in terms of a variational delay differential operator. Constructing a generalized Evans function, in infinite dimensions, it is shown how to derive stability criteria. Some examples are given when the criterion is fully explicit, e.g., for extreme Lax shocks. Additionally, connection is made with the alternative approach proposed by Chow, Mallet-Paret, and Shen (Journal of Differential Equations 1998), regarding the stability of traveling waves in general Lattice Dynamical Systems.     

Intralaboratory Repeatability of Residual Stress Determined by the Slitting Method

This paper presents repeated slitting method measurements of the residual stress versus depth profile through the thickness of identically prepared samples, which were made to assess repeatability of the method. Measurements were made in five 17.8 mm thick blocks cut from a single plate of 316L stainless steel which had been uniformly laser peened to induce a deep residual stress field. Typical slitting method techniques were employed with a single metallic foil strain gage on the back face of the coupon and incremental cutting by wire EDM. Measured residual stress profiles were analyzed to assess variability of residual stress as a function of depth from the surface. The average depth profile had a maximum magnitude of −668 MPa at the peened surface. The maximum variability also occurred at the surface and had a standard deviation of 15 MPa and an absolute maximum deviation of 26 MPa. Since measured residual stress exceeded yield strength of the untreated plate, microhardness versus depth profiling and elastic–plastic finite element analysis were combined to bound measurement error from inelastic deformation.     

Wave interactions and variation estimates for self-similar zero-viscosity limits in systems of conservation laws

We consider the problem of self-similar zero-viscosity limits for systems ofN conservation laws. First, we give general conditions so that the resulting boundary-value problem admits solutions. The obtained existence theory covers a large class of systems, in particular the class of symmetric hyperbolic systems. Second, we show that if the system is strictly hyperbolic and the Riemann data are sufficiently close, then the resulting family of solutions is of uniformly bounded variation and oscillation. Third, we construct solutions of the Riemann problem via self-similar zero-viscosity limits and study the structure of the emerging solution and the relation of self-similar zero-viscosity limits and shock profiles. The emerging solution consists ofN wave fans separated by constant states. Each wave fan is associated with one of the characteristic fields and consists of a rarefaction, a shock, or an alternating sequence of shocks and rarefactions so that each shock adjacent to a rarefaction on one side is a contact discontinuity on that side. At shocks, the solutions of the self-similar zero-viscosity problem have the internal structure of a traveling wave.     

The Potential of Ultrasonic Non-Destructive Measurement of Residual Stresses by Modal Frequency Spacing using Leaky Lamb Waves

This paper investigates the potential of ultrasonic non-destructive measurements of residual stresses using the modal frequency spacing method based on the interference spectrum of leaky Lamb waves as an alternative to the commonly used flight-time approach in ultrasonic methods. Extensive experiments were carried out to verify the viability and robustness of the technique using an instrumented leaky Lamb wave setup with uniaxial stressed samples and welded steel samples. To improve the signal-to-noise ratio, multiple sets of raw signals of specularly reflected and leaky Lamb waves were acquired and then averaged in the time domain. The acquired data in the time domain were then transformed into the frequency domain to form the interference spectrum of leaky Lamb waves with a good repeatability. The acoustoelastic coefficient of carbon steel is then derived from the measured relationship of wave velocity and applied stress. Finally, a welded steel plate was examined and residual stress was evaluated. The current work demonstrates the feasibility and the potential of the proposed method in measuring residual stresses in welded plates and thin-walled structures.     

The characterization of telephone cord buckling of compressed thin films on substrates

The topology of the telephone cord buckling of compressed diamond-like carbon films (DLC) on glass substrates has been characterized with atomic force microscopy (AFM) and with the focused ion beam (FIB) imaging system. The profiles of the several buckles have been measured by AFM to establish the symmetry of each repeat unit, revealing similarity with a circular buckle pinned at its center. By making parallel cuts through the buckle in small, defined locations, straight-sided buckles have been created on the identical films, enabling the residual stress in the film to be determined from the profile.It has been shown that the telephone cord topology can be effectively modeled as a series of pinned circular buckles along its length, with an unpinned circular buckle at its front. The unit segment comprises a section of a full circular buckle, pinned to the substrate at its center. The model is validated by comparing radial profiles measured for the telephone cord with those calculated for the pinned buckle, upon using the residual stress in the film, determined as above. Once validated, the model has been used to determine the energy release rate and mode mixity, G(ψ).The results for G(ψ) indicate that the telephone cord configuration is preferred when the residual stress in the DLC is large, consistent with observations that straight-sided buckles are rarely observed, and, when they occur, are generally narrower than telephone cords. Telephone cords are observed in many systems, and can be regarded as the generic morphology. Nevertheless, they exist subject to a limited set of conditions, residing within the margin between complete adherence and complete delamination, provided that the interface has a mode II toughness low enough to ensure that the buckle crack does not kink into the substrate.     

A numerical investigation of aerofoil boundary-layer manipulator profile for cruise-flight conditions

A computational study has been conducted to determine the variation of device drag with profile shape and angle of attack for aerofoil boundary-layer manipulators (LEBUs) operating at high subsonic Mach numbers. Calculations have been made at a free-stream Mach number of 0.80 for both symmetrical and asymmetrical NACA-00xx and 44xx series devices including an inverted cambered NACA-4409 profile. The LEBUs considered were located in a turbulent boundary-layer at a mid-chord heighth equivalent to 0.67 from the wall. The present investigations sought to confirm suggestions based upon experimental observations that there may be some advantage in replacing a symmetrical device by an inverted asymmetrical profile form.The computations were performed using an unstructured adaptive-mesh 3D Navier-Stokes code incorporating a Lam and Bremhorst low-Reynolds number two-equationk — turbulence model. The calculated flow field around a NACA-0009 aerofoil at zero angle of attack was initially verified against experimental interferometric data.The calculated device drag coefficient at zero incidence was 0.026 for the NACA-0009, similar to that measured in experiments. However predicted drag for an inverted NACA-4409 was 0.085, this being considerably higher than anticipated. The results suggested that a slightly positive angle of attack may help minimise device drag but neither profile is appropriate for use in transonic conditions. Improved results may be obtained from inverted flat-topped profiles designed to minimise losses associated with localised shocks.     

Validation of Mechanical Strain Relaxation Methods for Stress Measurement

Most validation studies of mechanical strain relaxation (MSR) methods for residual stress measurement rely on using the saw-tooth residual stress distribution resulting from four point bending and elastic–plastic deformation. Validation studies using simple applied stress profiles in rectangular steel beams are used in this work, together with beams subjected to elastic–plastic bending. Two MSR methods are explored, deep-hole drilling (DHD) and incremental centre hole drilling (ICHD). As well as a series of experiments, finite element analyses are conducted to determine the accuracy in the inversion of measured deformation to reconstruct stress. The validation tests demonstrated that apart from the applied stresses, the initial residual stresses also contribute even when samples are expected to be stress free. The uncertainty in measurement for the two MSR methods is determined, with the uncertainty in near surface measurement found to be significantly larger than uncertainty for interior measurement. In simple loading cases (and simple stress profiles) the uncertainty in measurement and hence the degree of validation is shown to be within about ±50 MPa for steel for “known” stress up to about 140 MPa. However, if the residual stress distribution is more complex there arises increased uncertainty in the predicted residual stress and lack of confidence between measurements methods.     

激光冲击修复后压力容器钢Q345R耐腐蚀及抗疲劳性能研究

对激光冲击强化后的压力容器材料Q345R钢的耐腐蚀性能和抗疲劳性能进行研究。通过电化学实验,并结合扫描电子显微镜分析其耐腐蚀性。结果显示,有吸收层保护和无吸收层保护激光冲击后,相较于原试样,耐腐蚀性分别提升5.8倍和2.6倍;微观实验结果表明经过激光冲击后腐蚀试样表面裂纹明显少于未处理试样。但随着冲击次数增加,耐腐蚀性有所下降。疲劳试验结果显示,相同应力条件下,腐蚀1和2 h的疲劳寿命相较于原试样降低36.8%和56.4%,经过一次或三次激光冲击后试件的疲劳寿命分别提升43.8%和198.2%,经XRD检测,激光冲击能在表面形成一定深度的残余压应力层并抑制裂纹扩展。     

An experimental investigation of the sonic criterion for transition from regular to Mach reflection of weak shock waves

The signal speed, namely the local sound speed plus the flow velocity, behind the reflected shocks produced by the interaction of weak shock waves (M _i < 1.4) with rigid inclined surfaces has been measured for several shock strengths close to the point of transition from regular to Mach reflection. The signal speed was measured using piezo-electric transducers, and with a multiple schlieren system to photograph acoustic signals created by a spark discharge behind a small aperture in the reflecting surfaces. Both methods yielded results with equal values within experimental error. The theoretical signal speeds behind regularly reflected shocks were calculated using a non-stationary model, and these agreed with the measured results at large angles of incidence. As the angle of incidence was reduced, for the same incident shock Mach number, so as to approach the point of transition from regular to Mach reflection, the measured values of the signal speed deviated significantly from the theoretical predictions. It was found, within experimental uncertainty, that transition from regular to Mach reflection occurred at the experimentally observed sonic point, namely, when the signal speed was equal to the speed of the reflection point along the reflecting surface. This sonic condition did not coincide with the theoretical value.     

Computational analysis of dense gas shock tube flow

Nonclassical phenomena associated with the classical dynamics of real gases in a conventional shock tube are studied. A TVD predictor-corrector (TVD-MacCormack) scheme with reflective endwall boundary conditions is used for the one-dimensional Euler equations to simulate the evolution of the wave field of a van der Waals gas. Depending upon the initial conditions of the gas, wave fields are produced that contain nonclassical phenomena such as expansion shocks, composite waves, splitting shocks, etc. In addition, the interactions of waves reflected from the endwalls produce both classical and nonclassical phenomena. Wave field evolution is depicted using plots of the flow variables at specific times and withx-t diagrams.     

Numerical study of breaking waves by a two‐phase flow model

A two‐phase flow model, which solves the flow in the air and water simultaneously, is presented for modelling breaking waves in deep and shallow water, including wave pre‐breaking, overturning and post‐breaking processes. The model is based on the Reynolds‐averaged Navier–Stokes equations with the k ?ε turbulence model. The governing equations are solved by the finite volume method in a Cartesian staggered grid and the partial cell treatment is implemented to deal with complex geometries. The SIMPLE algorithm is utilised for the pressure‐velocity coupling and the air‐water interface is modelled by the interface capturing method via a high resolution volume of fluid scheme. The numerical model is validated by simulating overturning waves on a sloping beach and over a reef, and deep‐water breaking waves in a periodic domain, in which good agreement between numerical results and available experimental measurements for the water surface profiles during wave overturning is obtained. The overturning jet, air entrainment and splash‐up during wave breaking have been captured by the two‐phase flow model, which demonstrates the capability of the model to simulate free surface flow and wave breaking problems.Copyright © 2011 John Wiley & Sons, Ltd.     

Generation of ramp waves using variable areal density flyers

Ramp loading using graded density impactors as flyers in gas-gun-driven plate impact experiments can yield new and useful information about the equation of state and the strength properties of the loaded material. Selective Laser Melting, an additive manufacturing technique, was used to manufacture a graded density flyer, termed the “bed-of-nails” (BON). A 2.5-mm-thick \(\times \) 99.4-mm-diameter solid disc of stainless steel formed a base for an array of tapered spikes of length 5.5 mm and spaced 1 mm apart. The two experiments to test the concept were performed at impact velocities of 900 and 1100 m/s using the 100-mm gas gun at the Institute of Shock Physics at Imperial College London. In each experiment, a BON flyer was impacted onto a copper buffer plate which helped to smooth out perturbations in the wave profile. The ramp delivered to the copper buffer was in turn transmitted to three tantalum targets of thicknesses 3, 5 and 7 mm, which were mounted in contact with the back face of the copper. Heterodyne velocimetry (Het-V) was used to measure the velocity–time history, at the back faces of the tantalum discs. The wave profiles display a smooth increase in velocity over a period of \(\sim \!\!2.5 \, {\upmu } \hbox {s}\), with no indication of a shock jump. The measured profiles have been analysed to generate a stress vs. volume curve for tantalum. The results have been compared with the predictions of the Sandia National Laboratories hydrocode, CTH.     

Modelling and experimental characterisation of the Lüders strain in complex loaded ferritic steel compact tension specimens

The use of 3D digital image correlation (DIC) has been used to capture the Lüders strains in a low carbon ferritic steel. Results were used to calibrate and compare with finite element (FE) results based on a constitutive plasticity model, capable of yield drop behaviour and therefore Lüders strains, by Zhang et al. (2001). Tensile tests were carried out at several strain rates to characterise the material behaviour. The results of these tests were used to fit parameters in the constitutive plasticity model. The FE model was then tested on a complex loading situation of in-plane compression of a compact tension (CT) specimen. The FE model predicts the shape and formation of the Lüders bands well. This FE model, using Zhang’s constitutive plasticity model, was used to predict the residual stress profile to compare with standard elastic–plastic isotropic hardening models with no yield point. The yield point reduced both the predicted peak tensile stress, at the notch root, and the amount of plastic strain. In regions where the plastic strain was of a similar size to the Lüders strain the stress profiles were perturbed from flat profiles predicted by the standard elastic–plastic hardening models.     

Formation of a jet and vortices behind a shock wave reflected from a concave body

A jet and vortices have been observed when a plane shock wave reflects from a concave body in a shock tube. If the cavity is deep enough then two reflected shocks appear near its edges. Air, carbon tetrafluoride (CF) and dichlorodifluoromethane (CClF) were chosen as test gases. The flow was visualized with the aid of a conventional shadow technique. Pressure measurements at the body surface were also obtained. Numerical studies have been conducted using a two-dimensional inviscid model. There is a good qualitative agreement between the experimental and numerical results. Received 8 February 1996 / Accepted 30 June 1997     

Measurement of the Residual Stress Tensor in a Compact Tension Weld Specimen

Neutron diffraction measurements have been performed to determine the full residual stress tensor along the expected crack path in an austenitic stainless steel (Esshete 1250) compact tension weld specimen. A destructive slitting method was then implemented on the same specimen to measure the stress intensity factor profile associated with the residual stress field as a function of crack length. Finally deformations of the cut surfaces were measured to determine a contour map of the residual stresses in the specimen prior to the cut. The distributions of transverse residual stress measured by the three techniques are in close agreement. A peak tensile stress in excess of 600 MPa was found to be associated with an electron beam weld used to attach an extension piece to the test sample, which had been extracted from a pipe manual metal arc butt weld. The neutron diffraction measurements show that exceptionally high residual stress triaxiality is present at crack depths likely to be used for creep crack growth testing and where a peak stress intensity factor of 35 MPa√m was measured (crack depth of 21 mm). The neutron diffraction measurements identified maximum values of shear stress in the order of 50 MPa and showed that the principal stress directions were aligned to within ~20° of the specimen orthogonal axes. Furthermore it was confirmed that measurement of strains by neutron diffraction in just the three specimen orthogonal directions would have been sufficient to provide a reasonably accurate characterisation of the stress state in welded CT specimens.     

Two-dimensional unstructured elastic model for acoustic pulse scattering at solid-liquid interfaces

Abstract. A numerical model to simulate elastic waves and acoustic scattering in two spatial dimensions has been developed and thoroughly tested. The model universally includes elastic solids and liquids. The equations of motion are written in terms of stresses, displacements and displacement velocities for control volumes constructed about the nodes of a triangular unstructured grid. The latter conveniently supports various geometries with complex external and internal boundaries separating sub-domains of different elastic properties. Theoretical dispersion for zero mode symmetric () and antisymmetric () waves in a plate has been reproduced numerically with high accuracy, thus verifying the method and code. Comparison of simulated acoustic pulse scattering at water-immersed steel plate with the respective experiments reveals a very good agreement in such delicate features as excitation of the surface (A) wave. The numerical results explain the peculiar location of the surface wave relative to the other ones in experimental registrations. Examples of acoustic pulse interactions with curvilinear metallic shells in water demonstrate flexibility of the method with respect to complex geometries. Potential applications as well as some directions for further improvement to the technique are briefly discussed. Received 5 September 2002 / Accepted 25 November 2002 Published online 4 February 2003 RID="*" ID="*"Permanent address: Ioffe Physical-Technical Institute, 26 Polytekhnicheskaya, 194021 St. Petersburg, Russia Correspondence to: P. Voinovich (e-mail: vpeter@scc.ioffe.ru)     

NUMERICAL PREDICTION OF SEMI-CONFINED JET IMPINGEMENT AND COMPARISON WITH EXPERIMENTAL DATA

The standard k–ε eddy viscosity model of turbulence in conjunction with the logarithmic law of the wall has been applied to the prediction of a fully developed turbulent axisymmetric jet impinging within a semi-confined space. A single geometry with a Reynolds number of 20,000 and a nozzle-to-plate spacing of two diameters has been considered with inlet boundary conditions based on measured profiles of velocity and turbulence. Velocity, turbulence and heat transfer data have been obtained using laser–Doppler anemometry and liquid crystal thermography respectively. In the developing wall jet, numerical results of heat transfer compare to within 20% of experiment where isotropy prevails and the trends in turbulent kinetic energy are predicted. However, stagnation point heat transfer is overpredicted by about 300%, which is attributed directly to the turbulence model and inapplicability of the wall function.