Local Strain Distribution Research Articles

A quantitative interphase model for polymer nanocomposites: Verification, validation, and consequences regarding size effects

The enhanced mechanical behavior of polymer nanocomposites with spherical filler particles is attributed to the formation of matrix-filler interphases. The nano-scale leads to particularly high interphase volume fractions while rendering experimental investigations extremely difficult. Previously, we introduced a molecular dynamics-based interphase model capturing the crucial spatial profiles of elastic and inelastic properties inside the interphase. This contribution demonstrates that our model captures polymer nanocomposites’ essential characteristics reported from experiments. To this end, we thoroughly verify and validate the model before discussing the resulting local plastic strain distribution. Furthermore, we obtain a reinforcement in terms of the overall stiffness for smaller particles and higher filler contents, while the influence of particle spacing seems negligible, matching experimental observations in the literature. This paper proposes a methodology to unravel the underlying complex mechanical behavior of polymer nanocomposites and to translate the findings into engineering quantities accessible to a broader audience and technical applications.

Transformation of 2D RVE Local Stress and Strain Distributions to 3D Observations in Full Phase Crystal Plasticity Simulations of Dual-Phase Steels

Crystal plasticity-based numerical simulations help understand the local deformation behavior of multiphase materials. It is known that in full phase simulations, the local 2-dimensional (2D) representative volume elements (RVEs) results are distinctly different from 3-dimensional (3D) RVEs. In this work, the difference in the results of 2D and 3D RVEs is investigated systematically, and the effect of magnification, total strain and composition are analyzed. The 3D RVEs of dual-phase (DP)-steel are generated using DREAM-3D. The 2D RVEs are the sliced surfaces of corresponding 3D RVEs for a direct pixel-to-pixel comparison of results. It is shown that the corresponding 3D distribution can be rapidly derived from the 2D result based on the alternative error and least square method. The interactive parameters for these processes are identified and analyzed for the ferrite phase, which provides information about the convergence. Examined by qualitative and quantitative statistical analysis, it is shown that the corresponding 2D distribution by the fourth iteration has a prominent similarity with the exact 3D distribution. The work presented here contributes toward solving the paradox of comparing local strain from 2D crystal plasticity (CP) simulations with the effective 3D specimen used for tests.

Characterization of local deformation and fracture behavior in ferrite + martensite dual-phase steels having different grain sizes

Low carbon dual-phase (DP) steels composed of soft ferrite and hard martensite have been widely used in the automotive industry due to their good strength-ductility balance and large strain hardening ability. DP steels have a wide variation in mechanical properties depending on several microstructural features such as grain size, phase fraction and distribution. Among them, the grain refinement of DP steels is known to be an effective option for enhancing mechanical performance in strength and ductility (especially post-uniform elongation). However, the exact reason for the significant improvement of post-uniform elongation by grain refinement has not been fully understood. It is considered that the characterization of local deformation behavior and micro-void formation/growth behavior in connection with microstructures is an essential approach for understanding the enhanced post-uniform elongation realized in the fine-grained DP specimen. In the present study, we prepared two kinds of DP specimens with mean ferrite grain sizes of 14.9 μm (coarse-grained DP) and 7.1 μm (fine-grained DP), and carefully investigated local strain distribution of tensile specimen and micro-void formation/growth behavior using digital image correlation (DIC) analysis and SEM observations. The fine-grained DP specimen exhibited a gradual strain localization after necking and had sufficient strain capacity that could endure against fracture. The fine-grained DP structure had a great number of micro-voids in the necked region, but almost all the micro-voids maintained a very small size, which was contrasted with the case of coarse-grained DP specimen containing very large-sized micro-voids. Such a significant difference in micro-void size/number characters between two kinds of DP specimens would be one possible reason for exhibiting greatly different post-uniform elongation behavior.

Strain localization at longitudinal weld seams during plastic deformation of Al–Mg–Si–Mn–Cr extrusions: The role of microstructure

The current work was motivated by the increasing use of hollow aluminum extruded profiles for automotive applications and the need for a better understanding of the mechanical response of extrusion seam welds. Two Al–Mg–Si alloys were studied, one without Mn and one with 0.5 wt%Mn and 0.15 wt%Cr. A high temperature homogenization was applied, resulting in a high density of α-Al(Fe,Mn)Si dispersoids in the Mn containing alloy, and an essentially dispersoid free microstructure in the other. The alloys were extruded through a simple porthole die (with two ports) to produce a strip with a centerline weld seam. The Mn free extrudate had a recrystallized grain structure whereas the Mn and Cr containing material was unrecrystallised. There were significant spatial variations of microstructure between the weld seam and surrounding regions, in particular the crystallographic texture. Tensile tests were conducted with the loading direction perpendicular to the weld seam using digital image correlation (DIC) to characterize the local strain distribution. Strain localization and final fracture occurred at weld seam for the unrecrystallized material whereas these occurred away from the weld line in the recrystallized case. The role of local crystallographic texture was examined through polycrystal plasticity simulations using the visco-plastic self consistent code (VPSC). These simulations indicated that the weld seam region was mechanically stronger than the surrounding region for the recrystallized alloy and correspondingly weaker for the unrecrystallized case, thereby rationalizing the experimental results of strain localization and final fracture location.

Superior mechanical properties and deformation mechanisms of a 304 stainless steel plate with gradient nanostructure

Spatially gradient microstructures have shown a promising application in enhancing strength-ductility synergy of engineering metals such as austenitic stainless steels. However, existing approaches are limiting in producing a thick gradient nanostructured (GNS) layer with a high strengthening capability, and the underlying deformation mechanisms are still not clear in GNS austenitic stainless steels. In this work, we developed a new approach, i.e., plate surface mechanical rolling treatment, to produce a bulk gradient nanostructure in a 304 stainless steel plate of ∼1.90 mm in thickness. Uniaxial tensile tests revealed that an ultra-high yield strength of ∼1073 MPa with a considerable uniform elongation of ∼21% was achieved in the GNS sample. Subsequently, the evolutions of microstructure, phase, microhardness, and local strain distribution were systematically studied in the GNS plate during tensile tests. The results demonstrated that the mechanical incompatibilities, relating with the gradient microstructure and martensite-enclosing-austenite domains, contribute to an extra strain-hardening capability, leading to the outstanding strength-ductility synergy in the GNS 304 stainless steel. Furthermore, analyses based on experimental observations and theoretical calculations revealed that dislocation activities, instead of deformation-induced martensite transformation, microstructure refinement, and twinning, play a dominant role in the strain-hardening mechanisms of the GNS plate during tension.

In-situ full-field measurements for 3D printed polymers during mode I interface failure

The fracture behavior of parts manufactured by fused filament fabrication (FFF) is highly driven by their mesoscale architecture characterized by the presence of weak interfaces between layers and filaments, likely to fail under loading. We propose an in-situ characterization approach to study the local phenomena driving the mode I interlayer and interfilament failure of FFF polymer specimens and support the development of a constitutive model for the interface damage. We provide full-field displacement and strain measurements by microstereoscopic digital image correlation (DIC) over a region of interest of around 4 × 3 mm2 in the proximity of the propagating crack for differently oriented interfaces. The high-resolution camera framework promotes the crack propagation monitoring and the crack length tracking until the specimen’s brittle failure. The local strain distribution reveals the distinctive mesoscale failure and damage mechanisms of 0°−0° and 0°−90° polylactic acid interlayer and interfilament interfaces. Overall, the 0°−90° stacking ensures higher fracture properties when compared to the 0°−0° counterpart, in agreement with the specimens’ force–displacement response recorded by the electromechanical testing device. Additionally, we propose a correlation between the strain contour plot heterogeneities observed for 0°−90° interlayer interfaces and 0°−0° interfilament interfaces and the specimens’ architecture inspected by scanning electron microscopy or X-ray computed tomography. Ultimately, the full-field measurements promote the development and validation of a constitutive model explicitly capturing the mechanical behavior of the interface.

Influence of strain and dislocations on GaSb/GaAs quantum dots: From nested to staggered band alignment

We investigate the influence of strain and dislocations on band alignment in GaSb/GaAs quantum dot systems. Composition profiles from cross-sectional scanning tunneling microscopy images are interpolated onto a finite element mesh in order to calculate the distribution of local elastic strain, which is converted to a spatially varying band alignment using deformation potential theory. Our calculations predict that dislocation-induced strain relaxation and charging lead to significant local variations in band alignment. Furthermore, misfit strain induces a transition from a nested (type I) to a staggered (type II) band alignment. Although dislocation-induced strain relaxation prevents the type I to type II transition, electrostatic charging at dislocations induces the staggered band alignment once again.

Electron microscopy for polymer structures

Abstract This paper reviews recent advances and perspectives of electron microscopy and its application to polymer hierarchical structures. Of the various kinds of hierarchical polymer structures, we placed particular emphasis on polymer nanocomposites and polymer crystals based mainly on our recent results. In those nanocomposites, the chemical bonding between the nanometer-size fillers and rubber matrix, a key contributor to the mechanical properties of the material, has been investigated by combining scanning transmission electron microscopy (STEM) with electron energy-loss spectroscopy (EELS). The position-dependent EELS spectrum with high spatial resolution of STEM successfully provided revealed the presence/absence of the chemical bonds across the interface. The mechanical properties and fracture mechanism of nanocomposites have been studied by combining structural observations made using transmission electron microscopy (TEM) with simulations. They have been further investigated using in situ TEM with a newly designed stretching holder, in which morphological changes, including cavity formation, were visualized and analyzed in terms of local strain distribution. The fracture processes of nanocomposite have been observed at nanometer resolution. The fundamental reinforcement mechanisms have been elucidated from morphological studies of nanocomposites under tensile deformation and during the fracture process. Moreover, nano-diffraction imaging, a position-resolved electron diffraction imaging with STEM, has been applied to a polymer crystal to evaluate the orientation of lamellar crystals at nanometer resolution. All these recent successes with radiation-sensitive polymer materials stemmed from developments made in electron optics and super-sensitive cameras used for advanced electron microscopy.

Investigation of the Crack Propagation in the Graphene/Synthetic Rubber Nanocomposite Materials with DIC Technique

This study investigated the crack propagation behavior of the graphene-reinforced synthetic rubber matrix nanocomposite materials. Graphene-filled rubber conductive nanocomposites developed within the scope of this study were obtained in two stages using mechanical mixers. The relationship between crack propagation and electrical resistance change was investigated using single-edge notched specimens in a tensile tester. Digital image correlation (DIC) technique was used to observe the crack resistance function depending on the local strain distribution. The results from the tests were evaluated to define the relationship between the crack length, the amount of conductive filler, and the change in electrical resistance. The sharp edges of the graphene nanoplatelets negatively affected the fracture resistance of the samples. In addition, it was observed that even at low strain values, gaps were formed in the areas close to the crack tip. The three-dimensional transmission network formed by graphene nanoplatelets dispersed in the matrix improved the electrical conductivity properties of the nanocomposites, so the relationship between crack propagation and electrical resistance change was determined.

Stages and Irregularities of Plastic Strain in Austenitic Stainless Steel within a Temperature Range of 143 < t < 420 k

This work aims at investigating the stages and irregularity of plastic strain in austenitic stainless steel 12Kh18N9T within a temperature range of 143 < T < 420 K. The localized plastic strain fronts at different stages of strain hardening have been visualized and monitored via digital speckle photography (DSP). This method consists in the high-accuracy recording of the displacement field via tracking any material surface changes and the subsequent comparison of speckle images acquired under uniaxial tension. The stress-strain diagrams were found to strongly vary with a decrease in temperature due to strain-induced-phase transition. The analysis of localized strain distributions revealed the emergence of a mobile system of equidistant strain localization foci at the strain hardening stage. The temperature dependence of plastic strain localization parameters at the linear strain hardening stage was established as well.

The deformation response of ultra-thin polymer films on steel sheet in a tensile straining test: the role of slip bands emerging at the polymer/metal interface

Abstract Forming of pre-coated sheet metal becomes of increasing importance in various fields of industrial application. In the recent years, ultra-thin plasma-polymer films have emerged as promising candidates as pre-treatments for steel sheet. Not much, however, is known about the forming behaviour of ultra-thin polymer coatings on ductile substrates, while an extensive literature exists for the reverse case, metal films on polymer, or brittle films on deformable substrates in general. For these cases, advanced models exist, mostly based on the so-called shear lag approximation. The heterogenous, highly localized strain and stress distribution, typical of ductile substrates, as well as out of plane displacements at the interface are disregarded, but cannot be neglected at the high strain levels of interest for elastic polymer films. This paper will focus on the role of slip bands on cracking of ultra-thin polymer films.

Assessing the structural behaviour of glued-laminated timber beams using distributed strain sensing

Global efforts to reduce the environmental impact of the construction industry have fueled the use of mass timber as a building material. However, the behaviour of mass timber elements is not fully understood, including the effects of localized anomalies (e.g., knots and joints) on global structural performance. To address this need, this study uses distributed fibre optic sensors (DFOS) to better understand the structural behaviour of mass timber elements through the testing of three glued-laminated (glulam) beams instrumented with DFOS under four-point bending. Results of the study demonstrated that DFOS data can be used to identify anomalies (e.g., knots, cracks, and finger joints) in glulam members, capture local strain distributions, and examine the influence of local effects on global structural response. Furthermore, distributed sensing was also found to be an effective tool to measure the in-situ elastic modulus of the timber material.

Experimental and numerical investigations of micro-meso damage evolution for a WC/Co-type tool material

Commercial Co/WC/diamond composites with 90vol.% Co also belong to hard metals and, as a kind of tool materials, are very useful. Their deformation behavior can be both ductile and quasi-brittle, determined by the diamond portion and local morphology. Another characteristic is that submicron-sized WC particles, possessing non-negligible strengthening influence due to the size effect, cannot be fully present in a representative microstructure. This work emphasizes the local damage evolutions’ dependence on microstructural features. Rice&Tracey damage and cohesive zone model describe the ductile and quasi-brittle damage behavior. The mechanism-based strain gradient plasticity takes the size effect of submicron-sized WC particles into consideration. Both real and artificial microstructures are used. Besides homogeneous boundary conditions (BCs), the periodic BCs are also applied in a 2D damage simulation. This work proves that FE models with two phases, the homogenized Co-WC matrix and diamond particles, can correctly predict damage evolution. FE results show that the WC phase has a higher mean stress value than the diamond phase, which is proved by the nano-indentation test. From FE simulation results, local hot spots appear in the matrix closed to sharp diamond corners/edges and crossing regions of shear bands. The experimental and numerical results are compared on micro and macro scales. For the local strain distribution and the damage development, numerical predictions match the reality well, even in morphological details. Furthermore, since the published data about WC-Co type tool materials with Co>50vol.% are rare, the obtained knowledge in this work also contributes to the data collection.

Position and electric field dependent local lattice strain detected by nanobeam x-ray diffraction on a relaxor ferroelectric single crystal

Under a static electric field, we present the scanning nanobeam x-ray diffraction of a relaxor ferroelectric single crystal. The x-ray intensity distributions of a Bragg peak in reciprocal space diffracted from local volumes on the surface of a $0.7\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}\ensuremath{-}0.3\mathrm{PbTi}{\mathrm{O}}_{3}$ (PMN-30PT) single crystal show position and electric field dependence. While the spatially averaged intensity distribution has a single peak corresponding to the average crystal structure, intensity distributions from each local volume have several strong sharp peaks and a weak broad peak, and show strong position dependence as the translation symmetry is broken in nano- to microscale. A static local lattice strain with spatially valuable lattice constants and nanodomains is responsible for peak splitting and heterogeneous crystal structure. The locally strained lattice exhibits a significant tensile lattice strain caused by an electric field, which is compatible with its large piezoelectric constant of approximately $2\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.16em}{0ex}}\mathrm{pC}/\mathrm{N}$. When the electric field surpasses the coercive field of 3 kV/cm, polarization switching causes a substantial shear lattice strain with intensity redistribution. Position dependence can also be seen in the piezoelectric constants and coercive fields calculated from x-ray diffraction data for each local location. The standard deviation of the local lattice strain distribution is $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ regardless of the electric field, which is greater than the piezoelectric lattice strain of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ caused by an electric field of 8 kV/cm. The enormous electric field induced lattice strain and fatigue-free polarization switching are enabled and facilitated by the nano- to microscale heterogeneous crystal structure with widely and continuously distributed local lattice strain.

Impact of conductor assembly indentation on the fatigue properties of copper power cable wires

The production process of high voltage power cables includes the assembly of the conductor, which is composed of different layer of independent wires wound in helixes of opposite pitch for each subsequent layer. Each wire, which has an initial constant round cross section and is close to annealed conditions, is wound around the previous layer and the assembled layers are passed through a calibrated die which compacts the wires together. This process creates periodically spaced indents on the inner side of the wires and work hardens the material in the indented sections and their immediate proximity. Both the local and global strain distribution related to static loads as well as the fatigue properties of the wires are impacted by such process and its consequent geometrical and material inhomogeneities. In this work, strain-control fatigue results of copper conductor wire are presented. The non-uniform strain distribution caused by the inhomogeneities inferred by their manufacturing process is investigated with the means of digital image correlation. The "indentation" process is modelled with the use of explicit finite elements and the deformation of the virtual specimen obtained is compared with the experimental results.

Analysis of the Reasons for the Tearing of Strips of High-Strength Electrical Steels in Tandem Cold Rolling.

High-strength non-oriented electro-technical steels with a low thickness possess excellent isotropy of electromagnetic and mechanical properties which is highly required in the production of high-efficiency electric motors. The manufacturing process of this type of steel includes very important and technologically complex routes such as hot rolling, cold rolling, temper rolling, or final heat treatment. The final thickness is responsible for the decrease in eddy-current losses and is effectively achieved during cold rolling by the tandem rolling mill. Industrial production of thin sheets of high-strength silicon steels in high-speed tandem rolling mills is a rather demanding technological operation due to the increased material brittleness that is mainly caused by the intensive solid solution and deformation strengthening processes, making the dislocation motion more complex. The main objective of this work was to investigate the distribution of local mechanical strains through the thickness of high silicon steel hot bands, generated during the cold rolling. The experimental samples were analysed by means of electron back-scattered diffraction and scanning electron microscopy. From the performed analyses, the correlation between the material workability and the nucleation of cracks causing the observed steel strip failure during the tandem cold rolling was characterized. Specifically, the microstructural, textural, misorientation, and fractographic analyses clearly show that the investigated hot band was characterized by a bimodal distribution of ferrite grains and the formation of intergranular cracks took place only between the grains with recrystallized and deformed structures.

Understanding asteroidal failure through quasi‐static compression testing and 3‐D digital image correlation of the Aba Panu (L3) chondrite

AbstractA comprehensive understanding of the mechanical strength and failure mechanisms of asteroids is essential for the development of hazard mitigation strategies and in situ resource extraction. In this study, the Aba Panu (L3) ordinary chondrite meteorite is investigated to understand its failure response under compressive loading. Compression experiments were conducted on ten 1 cm cubes under quasi‐static conditions in constant displacement control mode at room temperature. Three‐dimensional (3‐D) digital image correlation (DIC) was used to measure the full‐field deformation and strain. These data were used to determine the elastic modulus and local strain distribution, and investigate the effects of the mineralogical and structural heterogeneity on the crack formation and growth sites. Aba Panu exhibits brittle failure during compression with a range of failure strength from 361.7 to 578.0 MPa. Axial splitting and multiple fracturing occur during the uniaxial compressive state of stress. Ultrasonic tests were used to calculate elastic moduli from sound speeds and compared with the results of L‐type ordinary chondrites from the literature. Characterization results from electron microprobe analysis identified different elements and areal distribution of mineral phases and pre‐existing cracks. In general, the DIC results did not show correlations between crack initiation and specific mineralogical or textural components in this meteorite, such as chondrules or metals/sulfide grains, suggesting that the pre‐existing microcracks and porosity control the Aba Panu failure mechanisms.

Local Strain Distribution in ZnO Microstructures Visualized with Scanning Nano X‐Ray Diffraction and Impact on Electrical Properties

Three hexagonal ZnO rods, partly coated with gold or silver (Schottky contact) and aluminum (ohmic), are examined by current/voltage curves and scanning nano X-ray diffraction. This combination revealed a striking impact of the crystalline quality on the Schottky contact properties. Further details can be found in the article number 2100201 by Bridget M. Murphy and co-workers.

Distribution of two-level system couplings to strain and electric fields in glasses at low temperatures

The thermal, acoustic, and dielectric properties of glasses below 1 K are dictated by the interaction of two-level systems (TLS) with strain and electric fields. In a previous paper, we proposed a modified TLS model to quantitatively account for the universally small phonon scattering in glasses at low temperatures. A key ingredient of this model was a wide distribution of couplings between TLS and phonons, contrary to the standard model which assumes a single averaged value is sufficient. In this paper, we expand on this view and include couplings to strain as well as electric fields. We then compare our theoretical results to measurements obtained using superconducting qubits. We find that the predictions of the modified TLS model are more consistent with experiments than those of the standard model. For the distribution of couplings between TLS and the strain field, there is a better agreement with experiments if we include a random distribution of local strains. Such a distribution of local strains is consistent with those found from molecular dynamics simulations.

Developing a Lung Model in the Age of COVID-19: A Digital Image Correlation and Inverse Finite Element Analysis Framework.

Pulmonary diseases, driven by pollution, industrial farming, vaping, and the infamous COVID-19 pandemic, lead morbidity and mortality rates worldwide. Computational biomechanical models can enhance predictive capabilities to understand fundamental lung physiology; however, such investigations are hindered by the lung’s complex and hierarchical structure, and the lack of mechanical experiments linking the load-bearing organ-level response to local behaviors. In this study we address these impedances by introducing a novel reduced-order surface model of the lung, combining the response of the intricate bronchial network, parenchymal tissue, and visceral pleura. The inverse finite element analysis (IFEA) framework is developed using 3-D digital image correlation (DIC) from experimentally measured non-contact strains and displacements from an ex-vivo porcine lung specimen for the first time. A custom-designed inflation device is employed to uniquely correlate the multiscale classical pressure-volume bulk breathing measures to local-level deformation topologies and principal expansion directions. Optimal material parameters are found by minimizing the error between experimental and simulation-based lung surface displacement values, using both classes of gradient-based and gradient-free optimization algorithms and by developing an adjoint formulation for efficiency. The heterogeneous and anisotropic characteristics of pulmonary breathing are represented using various hyperelastic continuum formulations to divulge compound material parameters and evaluate the best performing model. While accounting for tissue anisotropy with fibers assumed along medial-lateral direction did not benefit model calibration, allowing for regional material heterogeneity enabled accurate reconstruction of lung deformations when compared to the homogeneous model. The proof-of-concept framework established here can be readily applied to investigate the impact of assorted organ-level ventilation strategies on local pulmonary force and strain distributions, and to further explore how diseased states may alter the load-bearing material behavior of the lung. In the age of a respiratory pandemic, advancing our understanding of lung biomechanics is more pressing than ever before.