Stereoscopic Digital Image Research Articles

Formability Characterization Using Curvature and Strain-Rate-Based Limit Strain Detection Methods Applied to Marciniak, Nakazima, and Stretch-Bend Tests

Despite advancements in the characterization of forming limit curves (FLCs) with the development of stereoscopic digital image correlation (DIC), there is still uncertainty in the accuracy of the limit strains, especially in forming operations with out-of-plane bending. The ISO12004-2:2008 standard offers a standardized approach to FLC determination but is not without limitations and is not always applicable to new materials and forming processes (e.g., warm forming, hot stamping). In the present work, a physically based limit strain detection technique is developed, termed the Enhanced Curvature Method (ECM), based on the sheet surface curvature evolution at the onset of necking in sheet formability testing. The ECM is applied to the characterization of 1.1 mm AA5182-O sheet using Marciniak, Nakazima, and stretch–bend characterization tests, and its limit strains are compared with those from the linear best-fit (LBF) local strain-rate approach and the ISO-12004 standard. The ECM considers the physical nature of necking in sheet forming with the aid of thresholds defined in terms of an imperfection metric analogous to the well-known Marciniak–Kuczynski (MK) imperfection factor. By quantifying the evolution of necking, FLCs of different safety margins can be readily generated, enabling a more intuitive selection for the factor of safety. For lower and upper ECM thresholds, the Marciniak plane strain limiting strain was determined to lie between 0.173 and 0.198, respectively, which is comparable to the analytical prediction of 0.194 and in general agreement with the published literature for AA5182-O. Similar plane strain limits were obtained using the ISO and LBF methods with values of 0.188 and 0.208, respectively. The same rankings in limit strain values between methods were observed for plane strain loading in Nakazima and stretch–bend tests.

Vibration of a thin panel exposed to ramp-induced shock-boundary layer interaction at Mach 2

Flight vehicles that operate in the supersonic regime can be subject to adverse fluid–structure interactions due to their lightweight design. The presence of geometric obstructions such as control surfaces or fins can induce shocks that can interact with the boundary layer, leading to flow separation. This work investigates experimentally the interaction between a compliant panel in a Mach 2 flow under a compression ramp-induced shock-wave/boundary-layer interaction (SBLI). Thin brass panels of different thickness are investigated in a wind tunnel. Tests are performed both with and without a 20° compression ramp installed. This direct comparison allows characterization of the effect of the SBLI on the system dynamics. High-speed stereoscopic digital image correlation (DIC) and fast-response pressure sensitive paint (PSP) are used to obtain simultaneous measurements of full field deformation and surface pressure of the panels. The panel vibration is dominated by the first bending mode. Despite the forcing of the separation shock foot, the presence of the SBLI does not significantly modify the operational deflection shape, frequency, and amplitude of the dominant vibration mode, beyond what is observed for the no-SBLI case. On the other hand, analysis of the shock foot motion shows that the shock primarily oscillates at the first natural frequency of the panel. This leads to the conclusion that the shock foot oscillation is driven by the panel vibration in a one-way coupling mechanism. The SBLI does modify the higher modes, which is likely due to localized forcing by the separation shock foot. Full-field surface pressure predictions are made using first order piston theory. Results show that the fluid–structure interaction is dominated by the large region of attached flow upstream of the shock foot.

Residual stress effects during additive manufacturing of reinforced thin nickel–chromium plates

Additive manufacturing (AM) is a powerful technique for producing metallic components with complex geometry relatively quickly, cheaply and directly from digital representations; however, residual stresses induced during manufacturing can result in distortions of components and reductions in mechanical performance, especially in parts that lack rotational symmetry and, or have cross sections with large aspect ratios. Geometrically reinforced thin plates have been built in nickel–chromium alloy using laser-powder bed fusion (L-PBF) and their shapes measured using stereoscopic digital image correlation before and after release from the base-plate of the AM machine. The results show that residual stresses cause potentially severe out-of-plane deformation that can be alleviated using either an enveloping support structure, which increased the build time substantially, was difficult to remove and wasted material, or using buttress supports to the reinforced edges of the thin plate. The buttresses were quick to build and remove, minimised waste but needed careful design. Plates built in a landscape orientation required out-of-plane buttresses while those built in a portrait orientation required both in-plane and out-of-plane buttresses. In both cases, out-of-plane deformation increased on release from the baseplate but this was mitigated by incremental release which resulted in out-of-plane deformations of less than 5% of the in-plane dimensions.

Experimental Investigation of Fluid-Structure Interaction in Mach 2 Flow Using Simultaneous High-Speed PIV and DIC

The fluid-structure interaction (FSI) of a compliant panel under a compression-ramp-induced shock-wave/boundary-layer interaction (SBLI) has been studied in Mach 2 flow. Simultaneous high-speed measurements of the velocity field and the panel displacement were conducted using 50 kHz particle image velocimetry (PIV) and 5 kHz stereoscopic digital image correlation (DIC). The mean effect of the panel displacement has been evaluated by monitoring the change in velocity profiles along the streamwise direction (x), upstream of the separated flow region. Streamwise (u) velocity near the panel surface has been shown to change its magnitude in response to the wall shape. Furthermore, the strong cross-correlation between fluctuations of the wall-normal panel displacement and the transverse (v) velocity can be explained by the flow remaining tangent to the wall surface as the panel deforms. This latter result is consistent with the panel motion being sufficiently low frequency compared to flow convective time scales that the flow is quasi-steady. In addition, assessment of the correlation between the separation shock position and panel displacement seems to suggest that when the panel is bulged down (concave up) at the downstream end of the panel, a larger separated flow is generated and the shock moves upstream. This observation remains speculative, but is consistent with the flow undergoing greater compression for the bulged down case.

Effect of Initial Temper on the Warm Forming Characteristics of a High Strength 7000-series Al-Zn-Mg-Cu Alloy

In this work, the formability of a developmental 7000-series copper containing aluminium alloy was assessed at room temperature (RT), 150°C, 175°C and 200°C in pre-aged (PA), peak-aged (T6) and overaged (T76) tempers using Nakazima tests with stereoscopic digital image correlation (DIC) strain measurement. The limit strains were identified using a novel curvature-based approach to detect the formation of an acute neck. The tensile mechanical properties in these warm forming processing routes were characterized with and without a paint bake cycle. Finally, a thermo-mechanical tensile simulator was used to evaluate the constitutive response of the PA and T76 tempers as a function of strain-rate and time at 175°C. Formability results found the selected PA temper to have a good room temperature formability and a mild positive response to the selected warm-forming cycles. The T6 and T76 tempers both exhibited increases in formability in response to warm forming. The PA temper had a significant positive response to short-duration warm forming and subsequent paint baking, with the yield strength increasing from 420 MPa to 512 MPa following this thermal cycle. For the T6 temper, the warm-forming cycle showed a trend characteristic of retrogression and re-aging, with the warm-forming cycle dropping the yield strength from 566 MPa to 534 MPa and the subsequent paint-bake re-aging to 554 MPa. The effect of aging during pre-heating prior to warm forming on the warm constitutive response of the PA and T76 tempers was also investigated. Both tempers exhibited rather different aging responses to short-duration thermal cycles. In the PA temper, this manifested as an increase in at-temperature yield strength and loss of hardening rate. In contrast, the T76 temper exhibited a drop in strength since this temper is already over-aged prior to warm forming. Both the PA and T76 tempers showed comparable at-temperature strain-rate sensitivity.

Characterizing environment‐dependent fracture mechanisms of ceramic matrix composites via digital image correlation

AbstractHere, we unveil a methodology for a novel assessment of the fracture mechanics of SiC/SiC ceramic matrix composites enabled by in situ stereoscopic digital image correlation to quantify in‐process flexural strain and crack opening displacement measurements. This technique isolates individual cracks on the composite surface as discontinuities in the spatial displacement field and correlates key fracture characteristics with the flexural strain of composite specimens during coupled four‐point bend / hermeticity testing. Fracture was observed along the specimen length, originating at the tensile underside and propagating around the circumference of the tubular specimens with generally uniform spacing. Multiple specimens were also tested after heat treatments to 1200°C in open air, in vacuum, and in helium for 48 h to evaluate the environmental effects on the fracture mechanisms of SiC/SiC composites, which revealed degradation of flexural properties after treatment in open air resulting in brittle failure. Indentation‐based fracture toughness measurements were performed, which confirmed a 25% reduction in toughness after open air heat treatment relative to the other heat treatments. This assessment indicated that significant oxidation may occur within the composites from these heat treatments and suggested that further protection of the composites may be necessary for high‐temperature applications.

Quantifying the effect of tow architecture variability on the performance of biaxially braided composite tubes

Targeted experiments are performed with stereoscopic digital image correlation to quantify the effect of irregular braid structure on the local surface mechanical response of carbon-fiber reinforced epoxy composite tubes. Virtual models comparing both nonuniform and uniform tow structure of the outer braid of each specimen are integrated into numerical simulations similar to experiments. Experimental and numerical results agree well. Statistical tests are used to support correlations between as-manufactured braid variation ranges to local increases in stress up to 18% compared to an ideal, uniform structure in the elastic regime. Results support improved manufacturing and modeling efforts of defect sensitive braided composites.

Modal Parameter Estimation of a Compliant Panel Using Phase-based Motion Magnification and Stereoscopic Digital Image Correlation

This paper demonstrates the use of broad-band phase based motion magnification (PMM) to improve the modal parameter estimation from high-speed stereoscopic digital image correlation (DIC). PMM is used as a diagnostic technique to investigate the free vibration response of a panel. The compliant panel, consisting of a thin polycarbonate sheet, forms a test section wall in a supersonic blow-down wind tunnel, where it is used to investigate supersonic fluid-structure interaction in the presence of shock wave boundary layer interaction. The panel is excited by an impact hammer and the transient deformation is captured using high-speed cameras. The original and motion-magnified images are input to a digital image correlation algorithm to calculate the out-of-plane deformation of the panel. The measured deformation is used to extract the modal parameters of the compliant panel. By using PMM as a preprocessing tool in a broad frequency band containing multiple structural modes, the signal to noise ratio of the measured deformation is improved. The use of PMM improves the estimated mode shapes, increasing the MAC value of the first mode compared to FEM predictions from 0.29 to 0.99. Motion magnification also improves the coherence between measured input force and panel deformation by up to 13% if suitable parameters are chosen.

Unveiling hermetic failure of ceramic tubes by digital image correlation and acoustic emission

AbstractA new, in situ hermeticity testing apparatus has been developed to allow helium leak evaluation of ceramic tubes, including nuclear‐grade SiC/SiC fuel cladding ceramic matrix composites (CMC), during four‐point bending with simultaneous monitoring of local deformation and damage, using stereoscopic digital image correlation (DIC) and acoustic emissions. The capabilities of the experimental apparatus are demonstrated using alumina, borosilicate glass, and 4130 steel tubes with representative cladding dimensions and then applied to study the deformation‐hermeticity relationship of SiC/SiC CMCs. Results of three CMCs appear to indicate that matrix cracking occurs near the deviation from linearity strain at strains ranging from 0.04% to 0.06% and is shortly followed by an initial loss of gas tightness by 0.09% bending strain. Leaking increased in distinct steps over 0.1%‐0.2% bending strain, and within this range, results indicate that prior to fiber fracture, it is likely possible to regain gas tightness upon unloading. This technique and uncovered hermetic failure behavior are intended to progress the standardization of a test methodology for nuclear reactor components and to begin to resolve the mechanisms controlling distinct steps of ceramic matrix composite failure.

Warm Forming Characteristics of AA7050-T6

The formability of AA7050 aluminum alloy sheet is characterized under isothermal forming conditions at room temperature and 150 °C. The material was tested in the T6 condition. Nakazima limiting dome height (LDH) tests in conjunction with stereoscopic digital image correlation (DIC) strain measurements are used for the formability assessment. Four-point forming limit curves (FLCs) were developed at the two test temperatures. AA7050-T6 is shown to respond positively to elevated temperature forming with a 0.19 major true limit strain for a 76.2 mm Nakazima specimen, for example, compared to 0.13 at room temperature. The current results for AA7050-T6 are compared to the formability of AA7075-T6 sheet tested under similar conditions; a slightly higher formability was observed for the AA7075-T6 alloy at the elevated temperature.

Strain distribution in rabbit eardrums under static pressure

Full-field strain maps of intact rabbit eardrums subjected to static pressures are presented. A stochastic intensity pattern was applied to 12 eardrums, and strain maps were measured at the medial site using a stereoscopic digital image correlation setup for pressures between −2 and 2 kPa. Ear canal overpressures induced circumferential orientated positive strains between manubrium and the eardrum border that increased almost linearly with pressure. Radially orientated negative strains were found at the border and manubrium. Ear canal underpressures caused negative circumferential strains between manubrium and the tympanic annulus but radially orientated positive strains at the borders. The magnitudes of these negative strains at underpressures were larger than those of positive strains at overpressures and were nonlinearly proportional to pressure. In three ears, strains were calculated with intact and removed cochlea. The effect of cochlea removal on the peak-to-peak strain was found to be no more than 3%.

Vertical Water Entry of a Flexible Wedge into Calm Water: A Fluid-Structure Interaction Experiment

Slamming water impact occurs frequently on high-speed craft and restricts the operating envelope of a vessel. One approach to understanding the hydroelastic nature of this phenomenon is to study the vertical impact of a V-shaped wedge on calm water, which models a single slamming event after a vessel has become partially airborne. The dynamic structural response of the bottom plate of a wedge dropped vertically (drop height = 7.9 cm) is investigated both experimentally and computationally. The experiments were conducted with a flexible bottom model at Virginia Tech. Pressure on the wedge bottom, rigid body motion (vertical acceleration and vertical position), and full-field out-of-plane deflection were measured. The out-of-plane deflection was measured using stereoscopic digital image correlation. Predictions on the hydrodynamic pressure field were made using Wagner's method, Vorus's method, and an unsteady Reynolds-averaged Navier-Stokes solver, all assuming a rigid plate. In the present work, the reconstructed pressure distribution from the experiment was used as the loading condition in a dynamic, linear finite element plate model (one-way coupled approach). Both the predicted pressure and predicted deflection were compared with the experiment. It was found that in the experiment, there is a slight reduction in the measured hydrodynamic pressure compared with predictions. This reduction in pressure leads to a reduction in the reactions at the plate edges, which get transmitted to the frames of the vessel. This slight reduction at small loading cases has the potential to be more noticeable when more severe slamming loads are encountered. 1. Introduction Slamming water impacts occur when a vessel impacts the water surface at high speed relative to the free surface. Water impact was first studied by von Karman (1929) with the application of seaplane landing. Water impact, as it pertains to slamming, gradually attracted increasing attention in the application of high-speed craft. The understanding of this phenomenon has been applied to the structural design and evaluation of the operational envelope of high-speed planing craft. Sailors also consider slamming a serious risk because it contributes to major injuries in addition to mission-related setbacks such as speed reduction or heading change. The present investigation of slamming can lead to the development of better design criteria for small craft.

Roll Control of Low-Aspect-Ratio Wings Using Articulated Winglet Control Surfaces

The use of tip mounted winglets with independently variable cant angles was investigated as a means of roll control on wings with an aspect ratio of one. Wind-tunnel testing was performed in which a six-axis force balance was used to measure the total aerodynamic load on wings with winglet control surfaces. Stereoscopic digital particle image velocimetry of the near-wake plane was used to show how the topology of the tip vortices changed with winglet deflection. Shifts in the location of the right tip vortex core are considered to be responsible for roll moment generation because they indicate changes in the symmetry of suction-side flow structures. All winglet deflections were observed to shift the right tip vortex core inboard, and thereby shorten the effective span of the wing. The effect of a winglet deflection may be approximated as a change in the wing aspect ratio and a lateral shift in the wing aerodynamic center. Prandtl’s lifting line theory provides a closed-form estimate for the reduction in lift caused by a winglet deflection. A geometrical argument was made to account for the induced roll moment. The right tip vortex core also shifts vertically, following the deflected wing tip. Vertical shifts in the right tip vortex result in an angle between the wing span line and a line connecting the two tip vortices. A positive angle is defined as the right tip vortex higher over the wing than the left, and it is accompanied by a positive roll moment. While in sideslip, the wing with no winglet deflection experiences a considerable roll moment as a result of a vertical and lateral shift in the two tip vortices. The articulated winglets are observed to partially mitigate these effects when the upstream winglet is actuated, and thus show promise as a direct means of disturbance rejection.

Measurement of CTOD along a surface crack by means of digital image correlation

The experimental measurement of fracture toughness and crack driving force are the main steps for the application of fracture mechanics methods in structural integrity assessment. Crack Tip Opening Displacement (CTOD), defined as the opening of a defect at its crack front upon loading a test specimen or structure, is one of the most important crack driving force parameters. However, due to its subsurface nature direct measurement of CTOD is very cumbersome. CTOD is commonly measured using single or double clip gauge techniques and applying a plastic hinge model. However, clip gauge CTOD calculations merely provide information related to the center of the defect. For the case of a finite-length surface breaking defect, where CTOD is variable along the defect front, exact knowledge of CTOD over the entire front is not possible by the clip gauge measurement techniques. In the present paper a novel technique is proposed based on full field three-dimensional profile measurement of the notched surface by means of stereoscopic Digital Image Correlation (3D-DIC) to measure the CTOD over the entire crack front. The proposed method is verified by measurement of silicone replicas cast inside the notch in addition to a supporting Finite Element (FE) investigation.

Experimental study of mode shifting in an asymmetrically heated rectangular plate

Modal shifting and jumping in thermally buckled plates has been investigated previously using computational models; however, relatively few experimental explorations have been reported. In this study, the modal shifts and jumps in a simple rectangular plate or panel were investigated using digital image correlation to obtain detailed mode shapes. One face of the planar panel, which was 219 × 146 mm, was speckled and viewed with a stereoscopic digital image correlation system using pulsed-laser illumination and with a laser vibrometer at a single point. The other face was heated using a set of 1 kW quartz lamps to produce a non-uniform temperature distribution which progressively increased from room temperature to around 760 K. An infra-red camera recorded the time-varying temperature distribution on the panel while it was excited with an electrodynamic shaker. A waterfall plot, or time-frequency spectrogram, showing natural frequencies as a function of time was generated, which highlighted the shifting response of the panel with temperature. The heating sequence was repeated and the panel excited at the natural frequencies identified in the waterfall plot, which permitted the corresponding mode shapes to be measured. These data showed that mode shifting and jumping was present with asymmetric heating, but not with spatially uniform heating, and was associated with thermally-induced buckling.

Limit Strain Characterization in an Aluminum Die-Quenching Process

This work examines the nature of the strain distributions and limit stains during die quenching of a 7000-series aluminum alloy sheet. Forming limit experiments using limiting dome height (LDH) specimens were performed under plane-strain loading conditions using a 100 mm hemispherical Nakazima punch. Strains were measured using in situ stereoscopic digital image correlation (DIC). Two forming processing routes were examined: (i) an intermediate quench and form (IQF) processing route in which the LDH coupons were solutionized, quenched to a preset temperature, and isothermally formed and (ii) a die-quench (DQ) process where the LDH coupons were solutionized, and quenched and formed simultaneously with room temperature (RT) tooling under non-isothermal conditions. The DQ processing route was devised to understand the formability of the alloy under practical die-quenching conditions, while the IQF route was meant to understand the influence of temperature on the formability of the material. The DQ processing route exhibited the best formability from a localization standpoint; however, it was found that at deformations in excess of 0.5 major true strain, an orange-peel defect was present. The IQF process with room temperature tooling may be comparable to a W-temper forming operation. For these conditions, significant Portevin-Le-Chatelier (PLC) bands were present and the formability was approximately 75% less than for the DQ process. All formability results are summarized and a discussion of the interpretation of forming limits under the diffuse necking conditions associated with elevated temperature forming is presented.

Wrinkling in engineering fabrics: a comparison between two different comprehensive modelling approaches.

We consider two ‘comprehensive’ modelling approaches for engineering fabrics. We distinguish the two approaches using the terms ‘semi-discrete’ and ‘continuum’, reflecting their natures. We demonstrate a fitting procedure, used to identify the constitutive parameters of the continuum model from predictions of the semi-discrete model, the parameters of which are in turn fitted to experimental data. We, then, check the effectiveness of the continuum model by verifying the correspondence between semi-discrete and continuum model predictions using test cases not previously used in the identification process. Predictions of both modelling approaches are compared against full-field experimental kinematic data, obtained using stereoscopic digital image correlation techniques, and also with measured force data. Being a reduced order model and being implemented in an implicit rather than an explicit finite-element code, the continuum model requires significantly less computational power than the semi-discrete model and could therefore be used to more efficiently explore the mechanical response of engineering fabrics.

Scalable measurements of tow architecture variability in braided ceramic composite tubes

AbstractThe performance of braided ceramic matrix composites has been shown to depend on the spatial arrangement of tows; therefore, a new class of tools is required to measure irregularities in the composite architecture for components with intricate geometries. We report a scalable and robust reconstruction technique built upon stereoscopic digital image correlation that is able to efficiently measure the position of tows in arbitrarily shaped composites. This method was applied to triaxially braided ceramic matrix composite tubes intended for use as nuclear fuel cladding, which revealed both long‐range “systematic” tow packing defects associated with the manufacturing process and short‐range “intrinsic” defects due to the braid architecture. These findings suggested that the character of tow spacing variation in braided composite tubes was substantially more complex than in planar woven composites. These measurements are expected to lead to improved processing of braided composites and to facilitate the design of statistically representative virtual specimens for finite element modeling.

Numerical and experimental investigation of the formability of AA6013-T6

AA6013 is an age-hardenable, aluminum alloy with the potential for structural applications in weight-sensitive automotive components. The alloy is at peak strength in the T6 temper, but exhibits relatively low room temperature formability. In an effort to avoid costly post-forming heat-treatments, warm forming of the AA6013 in the T6 temper is investigated in the current work. The experimental formability of the alloy is characterized from room temperature to 250°C through limiting dome height (LDH) tests with a Nakazima hemispherical punch and in-situ stereoscopic digital image correlation (DIC) strain measurement. A forming limit diagram (FLD) is generated from the application of a curvature-based necking criterion to the elevated temperature LDH test results. The evolution of the strain distribution prior to necking is explored using models of the plane strain LDH tests at room temperature and 200°C. At 200°C, strain rate effects are explored relative to the local temporal strain evolution. Modelling efforts include development of a Barlat Yld2000 yield surface to capture the anisotropy of the alloy and use of experimentally obtained isothermal flow-stress curves. The effects of different tensile gage lengths on flow-stress and yield surface calibration for warm tensile testing are discussed. The room temperature model was found to accurately depict the thinning strain distribution consistent with the “safe” thinning strain distribution at room temperature. At 200°C, it is shown that the temporal strain evolution is strongly influenced by strain-rate effects.

Geometry of an inflated membrane in elliptic bulge tests: Evaluation of an ellipsoidal shape approximation by stereoscopic digital image correlation measurements

Elliptic bulge tests are conducted on liver capsule, a fibrous connective membrane, associated with a field measurement method to assess the global geometry of the samples during the tests. The experimental set up is derived from a previous experimental campaign of bulge tests under microscope. Here, a stereoscopic Digital Image Correlation (DIC) system is used to measure global parameters on the test and investigate some assumptions made on the testing conditions which could not been assessed with microscopic measurements. In particular, the assumption of an ellipsoidal shape of the inflated membrane is tested by comparing the actual sample shape measured by stereoscopic DIC with an idealized ellipsoidal shape.Results indicate that a rather constant gap exists between the idealized and actual position. The approximation in the calculation of a macroscopic strain through analytical modeling of the test is estimated here. The study of the liver capsule case shows that important differences can be observed in strain calculation depending on the method and assumptions taken. Therefore, analytical modeling of mechanical tests through ellipsoidal approximation needs to be carefully evaluated in every application. Here the field measurement allows assessing the validity of these modeling assumptions. Moreover, it gives precious details about the boundary conditions of the bulge test and revealed the heterogeneous clamping, highlighted by strain concentrations.