Effect of strain rate on spatio-temporal behavior of Portevin–Le Châtelier bands in a twinning induced plasticity steel

Uniaxial tensile tests at three strain rates are performed with the aid of the digital image correlation (DIC) technique to experimentally investigate the spatio-temporal behavior of PLC bands in a twinning induced plasticity (TWIP) steel. The whole strain fields of tensile specimens are acquired throughout the tests. Significant serration crests corresponding to band nucleation are observed on the true stress vs. true strain curves derived from DIC results beyond a critical true strain. The work hardening exponent (n-value) increases from ∼0.08 to ∼0.5 when true strain increases to the critical true strain, and beyond that, the n-value exhibits serrations with increasing true strain. Two typical nucleation modes of Type-A Portevin–Le Châtelier (PLC) bands are observed in all tests. Nucleation and propagation of PLC bands are described in details based on these two nucleation modes of Type-A PLC bands. The PLC band orientation, which indicates the angle between the normal direction of a PLC band and tensile direction, fluctuates during propagation, and the fluctuation amplitude increases during the development of a localized necking band from a PLC band before fracture. In particular, the effect of strain rate on the kinematics of Type-A PLC bands (band strain, band width and band propagating speed etc.) in the TWIP steel is quantitatively analyzed, and a new algorithm based on the DIC results is presented which includes the elongating effect of tensile specimens during deformation to show the actual kinematics of Type-A PLC bands.     

Application of High Magnification Digital Image Correlation Technique to Micromechanical Strain Analysis

Abstract: This paper describes an experimental apparatus and its application for the full‐field measurement of heterogeneous strains at high magnifications. The apparatus consists of an image acquisition and analysis system, an optical microscope and a stable tensile stage. Magnified images of the specimen surface are acquired and analysed using the digital image correlation (DIC) method. The response of the heterogeneous microstructure of a nodular cast iron is investigated during a tensile test. Strains obtained by using the DIC method and averaged over the observation window correlate with strain measurements simultaneously obtained by using an extensometer. The strain maps of DIC reveal the heterogeneous development of plasticity in the nodular cast iron microstructure. The apparatus has the potential to investigate material behaviour at the microscopic scale.     

The role of grain size in static and cyclic deformation behaviour of a laser reversion annealed metastable austenitic steel

Different grain sizes were created in a metastable 17Cr‐7Mn‐7Ni steel by martensite‐to‐austenite reversion at different temperatures using a laser beam. Two fully reverted material states obtained at 990°C and 780°C exhibited average grain sizes of 7.7 and 2.7 μm, respectively. The third microstructure (610°C) consisted of grains at different stages of recrystallization and deformed austenite. A hot‐pressed, coarse‐grained counterpart was studied for reference. The yield and tensile strengths increased with refined grain size, maintaining reasonable elongation except for the heterogeneous microstructure. Total strain‐controlled fatigue tests revealed increasing initial stress amplitudes but decreasing cyclic hardening and fatigue‐induced α′‐martensite formation with decreasing grain size. Fatigue life was slightly improved for the 2.7‐μm grain size. Contrary, the heterogeneous microstructure yielded an inferior lifetime, especially at high strain amplitudes. Examinations of the cyclically deformed microstructure showed that the characteristic deformation band structure was less pronounced in refined grains.     

Size and geometry dependent tensile behavior of ultra-high-performance fiber-reinforced concrete

This research investigated direct tensile stress versus strain response of ultra-high-performance fiber-reinforced concrete (UHPFRC) with various sizes and geometries. The UHPFRC in this research contained 1% macro twisted and 1% micro smooth steel fibers by volume. The effects of gauge length, section area, volume and thickness of the specimens on the measured tensile response of the UHPFRC were experimentally discovered. The different sizes and geometries of specimens did not generate significant influence on the post cracking strength of UHPFRC whereas they produced clear effects on the strain capacity, energy absorption capacity and multiple cracking behavior of UHPFRC. The strain capacity, energy absorption capacity and the number of multiple micro cracks within unit length obviously decreased as the gauge length, section area and volume of UHPFRC specimens increased. In contrast, as the thickness of the specimen increased, different tendency was observed.     

Stress and strain based fracture forming limit curves for advanced high strength steel sheet

In this work, strain based fracture forming limit curve (FFLC) of advanced high strength (AHS) steel grade 980 was determined by means of experimental Nakajima stretch-forming test and tensile tests of samples under shear deformation. During the tests, a digital image correlation (DIC) technique was applied to capture the developed strain histories of deformed samples up to failure. The gathered fracture strains from different stress states were used to construct the FFLC. Subsequently, the FFLC in the strain space was transformed to a principal stress space by using plasticity theories. As a result, the fracture forming limit stress curve (FFLSC) of examined steel was obtained. Furthermore, fracture locus (FL) as a relationship between stress triaxialities and critical plastic strains was determined. Hereby, two anisotropic yield functions, namely, the Hill’48 and Yld89 model were taken into account and their effects on the calculated curves were investigated. To verify the applicability of the obtained limit curves, rectangular cup drawing test and forming tests of so-called Diabolo and mini-tunnel samples were performed. Obviously, the FFLSCs and FLs more accurately described the failure occurrences of 980 steel sheets than the FFLCs. In addition, it was found that the drawing depths predicted by the FLs and the Yld89 yield criterion slightly better agreed with the experimental results than those from the FFLSCs and the Hill’48 model, respectively.     

Determination of Ductile Fracture Parameters of a Dual‐Phase Steel by Optical Measurements

Marciniak–Kuczynski and Nakajima tests of the dual‐phase steel Docol 600DL ( www.ssab.com/ ) have been carried out for a range of stress‐states spanning from uniaxial tension to equi‐biaxial tension. The deformation histories of the specimens have been recorded by digital images, and the displacement and strain fields have been determined by post‐processing the images with digital image correlation software. The fracture characteristics of the material are presented by means of the stress triaxiality, the Lode parameter and the equivalent strain. These parameters are evaluated on the surface of the specimens based on the optical field measurements and assumptions regarding the mechanical behaviour of the material. Additionally the minor versus major principal strains up to fracture are presented. It is found that the material displays a significantly lower ductility in plane‐strain tension than in uniaxial tension and equi‐biaxial tension, and that it, in the tests exposed to local necking, undergoes large strains between the onset of necking and fracture. Fractographs of selected specimens reveal that fracture is due to growth and coalescence of voids that occur in localised areas governed by shear‐band instability.     

Fracture mechanism of AZ31 magnesium alloy processed by equal channel angular pressing comparing three point bending test and tensile test

A commercial magnesium alloy, AZ31 in hot-rolled condition, has been processed by equal channel angular pressing (ECAP) to get microstructure modified. Uniaxial tensile tests were conducted along the rolling/extrusion direction for as-received AZ31 alloy and ECAPed AZ31 alloy. Then, three point bending fracture tests were conducted for specimens with a pre-crack perpendicular to the extruded direction. Digital image correlation (DIC) technique was adopted to determine the deformation field around the crack tip. The fracture surfaces of the failed specimens after tensile tests and fracture tests were observed by Scanning Electron Microscope (SEM). To explore the deformation mechanism, the microstructure and texture of different regions on the deformed specimens were examined through electron backscatter diffraction (EBSD). The results show ECAP process improves both the tensile elongation and fracture toughness of AZ31 alloy. Different from the slip dominated deformation mechanism in the tensile test, deformation twinning presents in the deformation zone adjacent to the crack tip in the three point bending fracture tests. The fracture surface is characterized by co-occurrence of dimple and cleavage features.     

Experimental deformation analysis of an adhesively bonded multi-material joint for marine applications

The strength and deformation of full-scale adhesively bonded multi-material joints is studied in this paper. Four joints with a thick layer of methyl methacrylate adhesive (MMA) have been manufactured in shipyard conditions. In two specimens, cracks have been introduced at steel–adhesive and composite–adhesive interfaces. One cracked and one un-cracked specimen were subjected to quasi-static tensile testing; the two remaining specimens were stepwise loaded/unloaded with increasing load until failure. The strain in the adhesive layers was measured with digital image correlation (DIC). This showed a predominant shear deformation and dissimilar shear strain patterns for different bond lines. Fibre Bragg (FBG) sensors were used to monitor strains at steel and composite constituents and to detect the onset and evolution of damage in the un-cracked specimen. Strains measured by FBG sensors correspond well with DIC results at nearby regions. All specimens failed by delamination of the composite panel near the composite–adhesive interface.     

In Situ Nanoscale In-Plane Deformation Studies of Ultrathin Polymeric Films During Tensile Deformation Using Atomic Force Microscopy and Digital Image Correlation Techniques

The local, nanoscale deformation behavior of ultrathin polyethylene terephthalate (PET) and polyethylene naphthalate (PEN) films used as substrates in magnetic tapes was studied by atomic force microscopy (AFM) and digital image correlation (DIC) techniques. A custom-designed tensile stage was integrated with the AFM to perform uniaxial tension tests on the polymeric films in situ where the film surfaces were imaged simultaneously by AFM. The surface features on the PET and PEN films were used as reference patterns for the DIC processing. To improve the accuracy of the AFM imaging system for the application of the DIC method, a simple, cost-effective experimental procedure was established. Axial and transverse strain fields and Poisson's ratio maps with a spatial resolution of 78.13 nm were constructed via processing the AFM images of unstretched and stretched samples with the DIC software. Results from the AFM studies indicate that the deformation in both PET and PEN is nonuniform at the nanoscale. The nanoscale deformation mechanisms are discussed in conjunction with the structure of the PET and PEN films     

Assessing the Feasibility of Monitoring Strain in Historical Tapestries Using Digital Image Correlation

Abstract:  Digital image correlation (DIC) is used to monitor strain in a representative textile material and an historic tapestry. The validity of a 'map function' that allows 3D DIC displacement measurements to be obtained when the reference data are collected with a camera set-up different from that of the deformed data is assessed. An experiment was devised to study the effects of DIC processing parameters (interrogation cell size and overlap) on strain measurements, and to investigate if the textile contains adequate contrast for DIC to operate. The study shows that the textile's weave pattern can be used as the device for correlation. Long-term tests for monitoring creep strain using DIC both in the laboratory and in situ are presented. The results show good correspondence between strain changes in the tapestry and relative humidity.     

Towards the design of a new standard for composite stiffness identification

This paper presents a step towards the design of a novel test for simultaneous identification of all the stiffness components of orthotropic composite materials. A simulator was adopted to numerically simulate the whole identification process. Synthetic images were generated and then processed by Digital Image Correlation (DIC) to calculate the strain fields. The Virtual Fields Method (VFM) was used to identify the material stiffness parameters and error functions were finally defined to evaluate the identification error. Two steps of optimization were applied to obtain the best design variables of different specimens and the optimal DIC processing parameters. Four types of test configuration were simulated including short off-axis tensile test, short off-axis open-hole tensile test, off-axis Brazilian disc and off-axis unnotched Iosipescu test and the most promising configuration was identified.     

Determination of mechanical properties of PVC foam using a modified Arcan fixture

The design and development of a modified Arcan fixture (MAF) is described. The purpose of the fixture is to characterise polymer foam materials with respect to their tensile, compressive, shear and bidirectional mechanical properties. The MAF enables the application of pure compression or high compression to shear bidirectional loading conditions that is not possible with conventional Arcan fixtures. The tensile and shear behaviour to failure of a cross-linked Divinycell H100 PVC foam core material are studied using Digital Image Correlation (DIC). A detailed investigation of the parasitic effects of the fixture and misalignment of the fixture and loading machine are discussed. Thermoelastic Stress Analysis (TSA) is used to directly examine and validate the uniformity and symmetry of the stress fields obtained for both tensile and shear specimens. To account for the inhomogeneity of the strain field across the specimen cross sections, a “correction factor” for the measured “gauge section” surface strains has been determined using nonlinear finite element analysis (FEA). The outcome is a set of validated mechanical properties that are in excellent agreement with material property measurements conducted using conventional test tensile and shear test fixtures.     

Influence of fiber orientation on global mechanical behavior and mesoscale strain localization in a short glass-fiber-reinforced epoxy polymer composite during tensile deformation investigated using digital image correlation

Advanced polymer composites are used in various fields such as light-weight automobile, aerospace and bio-implant engineering owing to their extraordinary mechanical properties. The various fields of application and the complex microstructures of such materials require better understanding of their micromechanical behavior under external loads. In this work, the tensile testing is coupled with the novel technique of surface displacement mapping via digital image correlation (DIC) is utilized for resolving the mechanical behavior and spatial distribution of the plastic microstrains in an epoxy resin reinforced with 35 wt% short borosilicate glass fibers. The DIC method works by correlating the digital images of surface patterns before and after straining. The material exhibited a pronounced mechanical anisotropy at both macro and mesoscale, which depends on the alignment of the fibers relative to the external load. The underlying microstructure of the material explained formation of strain gradients during evolution of full-field strain fields. The levels of localized strain are higher than the global failure strain of the material. Also, scanning electron microscopy (SEM) on the fracture surfaces revealed the multiple failure mechanisms of the material as a function of the fiber orientation.     

Comparative study on local and global mechanical properties of 2024 T351, 2024 T6 and 5251 O friction stir welds

The effect of the microstructure heterogeneity on the global and local tensile properties of friction stir welded joints in 5251 (O temper) and AA2024 (T351 and T6 tempers) aluminium alloys has been investigated. Micro-tensile tests parallel to the welding direction have been carried out in the regions representative of the main microstructural zones. The digital image correlation technique (DIC) has been used during transverse tensile tests for mapping the strain distribution and to determine the local stress–strain curves. A 3-D finite elements model has been developed to predict the weld behaviour from the tensile curves of the individual regions of the weld.The tensile properties of the 5251 O weld are relatively homogeneous leading to high ductility and fracture in the base material. In contrast, the tensile properties of the various regions of the 2024 T351 and 2024 T6 welds are very heterogeneous and essentially controlled by the state of precipitation. The thermo-mechanically affected zone is the weakest region where the strain localises during a transverse tensile test. The 2024 T6 base material is stronger than the 2024 T351 alloy, leading to a more pronounced strain localisation during transverse tensile tests and a lower overall ductility. Local tensile data obtained by strain mapping are in good agreement with the curves obtained by micro-tensile tests, and these results can be safely used in a finite elements model to predict the behaviour of the overall weld assembly.     

An iterative procedure for determining effective stress–strain curves of sheet metals

An iterative correction procedure using 3D finite element analysis (FEA) was carried out to determine more accurately the effective true stress–true strain curves of aluminum, copper, steel, and titanium sheet metals with various gage section geometries up to very large strains just prior to the final tearing fracture. Based on the local surface strain mapping measurements within the diffuse and localized necking region of a rectangular cross-section tension coupon in uniaxial tension using digital image correlation (DIC), both average axial true strain and the average axial stress without correction of the triaxiality of the stress state within the neck have been obtained experimentally. The measured stress–strain curve was then used as an initial guess of the effective true stress–strain curve in the finite element analysis. The input effective true stress–strain curve was corrected iteratively after each analysis session until the difference between the experimentally measured and FE-computed average axial true stress–true strain curves inside a neck becomes acceptably small. As each test coupon was analyzed by a full-scale finite element model and no specific analytical model of strain-hardening was assumed, the method used in this study is shown to be rather general and can be applied to sheet metals with various strain hardening behaviors and tension coupon geometries.     

Application of a Multi‐Camera Stereo DIC Set‐up to Assess Strain Fields in an Erichsen Test: Methodology and Validation

Abstract: A multi‐camera stereo digital image correlation (MC‐DIC) set‐up is presented to obtain full displacement and strain fields of a sheet‐metal specimen subjected to an Erichsen test. The set‐up is composed of several conventional stereo DIC systems (two camera set‐up), each of which tracks the deformation of an aspect of the specimen. The individual measurements, including the geometries and the displacements, are then converted to the same reference frame to integrate into a global view. Afterwards, the strain is calculated based on the composed displacement field. It is found that the geometry and the displacement fields of the bulged specimen are ideally stitched, and smooth strain fields are obtained. The influences of the reference frame transformation and the stitching procedure on the MC‐DIC measurement are investigated. A rigid motion test is performed to validate the displacement measurement. It is discussed that the global field is more reliable than the individual measurements for this test set‐up.     

Adaptation of the strain measurement in textile reinforced cementitious matrix composites by distributed optical fibre and 2D digital image correlation

The study presented in this paper aims to adapt and calibrate two strain measurement techniques used for textile reinforced cementitious matrix composites (TRCMCs): distributed optical fibres and 2D digital image correlation (DIC). These composites exhibit tensile behaviour characterised by a succession of transverse cracks along specimens. During the tensile test, out-of-plane parasitic displacements may occur due to the geometry of specimens and possible imperfections of the test method. These phenomena interfere with the measurement of the strain sensors, leading to loss of results and parasitic strain. In order to eliminate them and to finely analyse the complex behaviour of TRCMCs, a test methodology and experimental approach are proposed for optical fibres, and a practical and simple solution is proposed to quantify the parasitic strains of the 2D DIC. For optical fibres, Rayleigh backscatter is used, allowing a millimetric spatial resolution and a high recording frequency. For the DIC, required equipment is used, and the results are processed through existing commercial software.     

Validation of finite-element models using full-field experimental data: Levelling finite-element analysis data through a digital image correlation engine

Full-field data from digital image correlation (DIC) provide rich information for finite-element analysis (FEA) validation. However, there are several inherent inconsistencies between FEA and DIC data that must be rectified before meaningful, quantitative comparisons can be made, including strain formulations, coordinate systems, data locations, strain calculation algorithms, spatial resolutions and data filtering. In this paper, we investigate two full-field validation approaches: (1) the direct interpolation approach, which addresses the first three inconsistencies by interpolating the quantity of interest from one mesh to the other, and (2) the proposed DIC-levelling approach, which addresses all six inconsistencies simultaneously by processing the FEA data through a stereo-DIC simulator to ‘level' the FEA data to the DIC data in a regularisation sense. Synthetic ‘experimental' DIC data were generated based on a reference FEA of an exemplar test specimen. The direct interpolation approach was applied, and significant strain errors were computed, even though there was no model form error, because the filtering effect of the DIC engine was neglected. In contrast, the levelling approach provided accurate validation results, with no strain error when no model form error was present. Next, model form error was purposefully introduced via a mismatch of boundary conditions. With the direct interpolation approach, the mismatch in boundary conditions was completely obfuscated, while with the levelling approach, it was clearly observed. Finally, the ‘experimental' DIC data were purposefully misaligned slightly from the FEA data. Both validation techniques suffered from the misalignment, thus motivating continued efforts to develop a robust alignment process. In summary, direct interpolation is insufficient, and the proposed levelling approach is required to ensure that the FEA and the DIC data have the same spatial resolution and data filtering. Only after the FEA data have been ‘levelled' to the DIC data can meaningful, quantitative error maps be computed.     

In situ observation of crack nuclei in poly-granular graphite under ring-on-ring equi-biaxial and flexural loading

Fracture tests of graphite are known to exhibit sensitivity to stress state, such as a difference between their flexural and tensile strengths. Bi-axial tensile and flexural loading are representative of the stress states in some regions of graphite components in nuclear fission reactors, where loading develops from fast neutron irradiation-induced dimensional change and thermal strains. Study of the behaviour of the inherent defects that determine strength variability requires in situ observation of crack nucleation. To this end, digital image correlation can be used to monitor the evolution of displacement fields and hence the cracks on the surface of large samples whilst under load. In this study, a ring-on-ring flexural test setup was developed to apply equi-biaxial tensile stress to large disc specimens of graphite along with the conventional four-point-bend test. A 17% reduction in mean flexural strength was observed for the equi-biaxial loading, relative to uniaxial loading. DIC was used to characterise the observed fracture nuclei. Linear elastic fracture mechanics analysis was shown to be inadequate to explain the strength reduction. It is suggested that fictitious crack models, originally developed to simulate the behaviour of concrete structures, can be utilised to explain the behaviour.