Strain Field Distribution Research Articles

Experimental and Numerical Analysis of the Stress State Produced by a Circular Hole Concentrator

The paper proposes the analysis of strain and stress state, through experimental and numerical means, of a circular hole type concentrator. The strain state is analyzed through the microscopic Digital Image Correlation technique, due to the small scale of the samples, whose calibrated region is 10x8 mm. The numerical analysis is conducted using the Finite Element Method, through a static structural analysis, using a linear-elastic material model. The results from the two procedures are compared by means of strain field distribution around the stress concentrator and stress variation at the concentrator peak cross section. For validation, the analytical gross stress concentrator of the problem is used as baseline, Ktg. The results show that accurate reading can be achieved on this small scale. Additionally, the experimental method has also successfully identified crack initiations and propagations on the tested samples, significantly smaller than 1 mm, which can reveal future fracture mechanics analysis and supply data to models adapted to microscopic scale phenomena.

Bulge test technique and digital image correlation for the determination of the biaxial behavior of polymeric films

Abstract Materials can display multiple mechanical behaviors when they are biaxially stressed. In this research work, films obtained through the blowing process were investigated in order to compare the mechanical properties and behavior of the film under uniaxial and biaxial stress conditions. Bulge test coupled with a continuous full-field strain measurement was undertaken in order to characterize polymeric film in a biaxial stress state. As far as this study is concerned, a laboratory-made pneumatic bulge test machine was used for the determination of the biaxial behavior of a 50 μm thickness PLSF (modified PLA) film. 3D-digital image correlation (3D-DIC) technique was used in order to compute the strain field continuously during the test. Tensile test was equally performed on the film along its machine direction (MD) and transverse direction (TD). Strain field distribution in the film sample was analyzed and compared in both tests. The tensile test results displayed an isotropic behavior of the film in both directions. However, a difference in the strain at break was noticed because of the thickness instability along the TD. The comparison between uniaxial and biaxial properties resulted in almost the same properties with respect to the Young Modulus as well as the tensile strength.

Development of Fiber-Bragg-Grating-Integrated Artificial Embedded Tendon for Multifunctional Assessment of Temperature, Strain, and Curvature.

This paper presents the development and application of an optical fiber-embedded tendon based on biomimetic multifunctional structures. The tendon was fabricated using a thermocure resin (polyurethane) and the three optical fibers with one fiber Bragg grating (FBG) inscribed in each fiber. The first step in the FBG-integrated artificial tendon analysis is the mechanical properties assessment through stress-strain curves, which indicated the customization of the proposed device, since it is possible to tailor the Young's modulus and strain limit of the tendon as a function of the integrated optical fibers, where the coated and uncoated fibers lead to differences in both parameters, i.e., strain limits and Young's modulus. Then, the artificial tendon integrated with FBG sensors undergoes three types of characterization, which assesses the influence of temperature, single-axis strain, and curvature. Results show similarities in the temperature responses in all analyzed FBGs, where the variations are related to the heterogeneity on the polyurethane matrix distribution. In contrast, the FBGs embedded in the tendon presented a reduction in the strain sensitivity when compared with the bare FBGs (i.e., without the integration in the artificial tendon). Such results demonstrated a reduction in the sensitivity as high as 77% when compared with the bare FBGs, which is related to strain field distributions in the FBGs when embedded in the tendon. In addition, the curvature tests indicated variations in both optical power and wavelength shift, where both parameters are used on the angle estimation using the proposed multifunctional artificial tendon. To that extent, root mean squared error of around 3.25° is obtained when both spectral features are considered. Therefore, the proposed approach indicates a suitable method for the development of smart structures in which the multifunctional capability of the device leads to the possibility of using not only as a structural element in tendon-driven actuators and devices, but also as a sensor element for the different structures.

Atomistic approach to the strain field in finite-sized heterostructures

The numerical code AS_LBFG_v2 developed to simulate the atomic elastic relaxation in finite-sized heterostructures is introduced. To minimize the elastic energy the L-BFGS algorithm is utilized. A user-defined initial atomic configuration, without restrictions on the shape of the matrix embedding quantum dot (QD), can be implemented in the code. By enlarging the pyramidal QD heterostructure towards mesoscopic size, the code generates a strain field distribution similar to that obtained by continuum model for weakly polar semiconductors. The strain field obtained for semi-torus, and spherical shape QDs embedded in finite-sized matrices is also presented. The dependence of the strain field on the cap thickness and the distribution of misfit dislocations in the relaxed configuration are simulated by the code. Program summaryProgram titles:AS_LBFG_v2, AS_Calc_v2CPC Library link to program files:https://doi.org/10.17632/53dshkskct.1Code Ocean capsule:https://codeocean.com/capsule/5342364/tree/v1 and https://codeocean.com/capsule/9050452/tree/v1Licensing provisions: MIT licenseProgramming language: FORTRANNature of problem: An initial constraint atomic configuration of a heterostructure is relaxed by imposing Keating's elastic interaction. The strain field and distribution of misfit dislocations are simulated for various quantum dot shapes and heterostructure materials.Solution method: The elastic energy of the heterostructure is minimized by an L-BFGS algorithm. The strain field is calculated by a discrete mathematical expression at each atomic location.

Elastic Field Evolution in Al–X (X = Sc, Zr, Er) Alloy During Heat Treatment, Insights From 3D-Multiphase Field Study

Abstract Microstructural evolution and resulting stress, strain, and concentration field distribution during Al3X (X = Sc, Zr, Er) precipitation in Al matrix are investigated in this work using the 3D-multiphase field method. Depending on the heat treatment, modulus mismatch, lattice parameter mismatch, and interfacial free energy, precipitate developed to rhombicuboctahedron, and near cuboidal morphologies. The composition distribution and Al–Al3X transformation driving force map identified a difference in precipitation kinetics for each alloy. The precipitation mechanism in the three systems is analyzed in detail with temporal evolution plots of energy components during phase transformation. Al3Er precipitate exhibits the highest growth rate due to Er's high diffusivity and significant lattice parameter mismatch in the Al–Er system. The system has a high chemical and elastic driving force for particle growth, thus attaining quasi-static equilibrium at a relatively lower temperature and time. Therefore, this system observes high magnitude stress, strain, and strain energy field around the Al matrix. The theoretical simulation results obtained from the present study will benefit aluminum multicomponent alloy design for high-strength applications.

Strain and crystallographic identification of the helically concaved gap surfaces of chiral nanoparticles

Identifying the three-dimensional (3D) crystal plane and strain-field distributions of nanocrystals is essential for optical, catalytic, and electronic applications. However, it remains a challenge to image concave surfaces of nanoparticles. Here, we develop a methodology for visualizing the 3D information of chiral gold nanoparticles ≈ 200 nm in size with concave gap structures by Bragg coherent X-ray diffraction imaging. The distribution of the high-Miller-index planes constituting the concave chiral gap is precisely determined. The highly strained region adjacent to the chiral gaps is resolved, which was correlated to the 432-symmetric morphology of the nanoparticles and its corresponding plasmonic properties are numerically predicted from the atomically defined structures. This approach can serve as a comprehensive characterization platform for visualizing the 3D crystallographic and strain distributions of nanoparticles with a few hundred nanometers, especially for applications where structural complexity and local heterogeneity are major determinants, as exemplified in plasmonics.

Fatigue damage monitoring of composite laminates based on acoustic emission and digital image correlation techniques

Timely and effective health evaluation of carbon fiber reinforced polymer (CFRP) structures under dynamic fatigue loading is one of the key issues of CFRP in practical engineering applications. This paper uses a combination of acoustic emission (AE) and digital image correlation (DIC) to study the fatigue behavior of CFRP open-hole laminated beams with different stacking sequences under pure tensile loading, and analyze the influence of different damage mechanisms on the ultimate fatigue failure of the specimens. Two parameters, AE hit rate and absolute AE energy, are used to characterize the stiffness degradation behavior of CFRP structures. The strain field distribution characteristics during the damage failure of specimens with different stacking sequences are discussed in association with DIC. Based on the data obtained by AE and DIC, the damage modes of two types of layered CFRP laminated beams are identified by combining principal component analysis (PCA) and the K-means++ algorithm. The clustering results are consistent with the microscopic image results of the fracture surface. The identified modes are employed to characterize the dynamic evolution of fatigue damage in CFRP, and the contribution of different damage modes to the ultimate fatigue failure of the specimens is analyzed using cumulative damage index (CDI) values.

Nucleation of Threading Dislocations in 4H-SiC at Early Physical-Vapor-Transport Growth Stage

In this work, we identify the nucleation mechanism of threading dislocations (TDs) associated with stacking faults (SFs) and 15R-SiC at the early growth stage of 4H-SiC single crystals grown by the physical vapor transport (PVT) technology. By combining molten KOH etching and photochemical etching, we successfully reveal etch pits of TDs and linear etch patterns of SFs on the (112̅0) surface of 4H-SiC single crystals. Systematic investigations based on transmission electron microscopy (TEM) observations and Raman analysis indicate that the Si–C bilayer stacking sequence of SFs is (3, 2) in Zhdanov’s notation. The accumulation of SFs (3, 2) gives rise to the polymorph fluctuation and thus the formation of 15R-SiC at the early PVT growth stage of 4H-SiC single crystals. Quantitative stress analyses indicate that the strain field distributions along the SFs (3, 2) and the 15R-/4H-SiC interfaces are inhomogeneous, which give rise to the nucleation of TDs and low-angle grain boundaries (LAGBs), respectively. The nucleation of LAGBs releases the high stress at the 15R-/4H-SiC interface, which facilities the following 4H-SiC single-crystal growth. Our work indicates that the avoidance of polymorph fluctuation is important to the reduction of TDs at the early growth stage of PVT-grown 4H-SiC single crystals.

Multi-stage finite element modeling of the deformation behavior during ultrasonic-assisted incremental sheet forming

The incremental sheet forming (ISF) has the characteristics of high flexibility, short lead time and enhanced formability. However, it still needs to be further improved in the aspect of forming quality (e.g. geometric accuracy and surface finish). The introduction of ultrasonic energy field may improve the deformability of sheets and the performance of parts, and reduce the load during sheet metal forming. The present work aims to meticulously investigate the influence of ultrasonic vibration on the deformation mechanism of material in several periods. First, based on an improved material constitutive model which considers both the thermal activation and dislocation density evolution process, a multi-stage finite element model of UISF was established. In particular, the multi-stage finite element model of UISF is divided into two stages, the full contour forming stage and the local forming stage, in which a transient simulation with high frequency output was realized. The influence of vibration parameters on the forming force as well as the distribution of stress and strain field in the forming process was comprehensively analyzed. The results show that the ultrasonic vibration reduces the forming force obviously (53% at amplitude of 10 µm), which is due to the dynamic impact effect and acoustic softening effect. Four distinct stages, approaching, loading, unloading and departing, are observed in a single vibration period. The dynamic impact effect of ultrasonic vibration changes the contact state between sheet and forming tool and causes the continuous propagation of dynamic oscillatory stress wave inside the material (propagate to the entire plate at 0.002 s), which leads to the significant change of stress and strain field. At the same time, the maximum stress is significantly reduced (73% at amplitude of 10 µm). By applying ultrasonic vibration on the stress-strain field, it is found that these vibrations mainly act on the contact region between the sheet and forming tool. The high frequency vibration makes smooth stress distribution along the path as well as spread over the whole sheet area to create a uniform distribution. Benefitting from the smooth stress distribution, the vibration also promotes greater formability with good forming quality and the plastic deformation mainly occurs in the side wall deformed area. The present work provides a practical simulation approach to study the transient deformation behavior of materials under the ultrasonic field.

Integrated experimental and modeling approach for hot deformation behavior of Co–Cr–Fe–Ni–V high entropy alloy

The study aims to investigate the hot deformation behavior of Co–Cr–Fe–Ni–V high entropy alloy (HEA) at temperatures ranging from 1073 K to 1373 K and strain rates of 0.001, 0.01, 1, and 10 s−1, and to generate processing maps using dynamic materials modeling (DMM) to identify the optimum processing domain for industrial applications. The material's hardening and softening characteristics are also explored under various hot working conditions. Deformation twinning is observed in materials deformed at 0.1 s−1 at 1273 K and 1373 K, contributing to their observed hardening. The mean free path of dislocation defines the material's strength, and the transition point from dynamic recovery to dislocation-dislocation or dislocation-solute interaction occurs when the mean free path of dislocation reaches its lowest value. The inhomogeneity in the deformed sample is correlated with the strain field distribution using an integrated approach using finite element method (FEM) modeling and electron backscattered diffraction (EBSD) results. EBSD characterization reveals the presence of deformation bands and annealing twins at low and high temperatures, respectively. Additionally, an artificial neural network (ANN) model is proposed to predict the hot deformation behavior of Co–Cr–Fe–Ni–V HEA, with promising results, as evidenced by a correlation coefficient (R) of 0.9983 and an average absolute relative error (AARE) of 2.71% on the test dataset.

An evaluation method for experimental necking detection of automotive sheet metals

In sheet metal stamping, the occurrence of strain localization in a deformed sheet is considered a failure. As so, sheet metal’s formability is conventionally evaluated using the Forming Limit Diagram (FLD), which separates the principal strain space into safety and unsafety regions by a Forming Limit Curve (FLC). This study presents an evaluation method for detecting strain localization based on Digital Image Correlation (DIC) during the experiment. The commercial DIC software ARAMIS is adopted to monitor the strain-field distribution on the deformed specimen’s surface. A detailed analysis of the proposed method is presented considering Nakajima tests conducted for two automotive sheet metals: AA6016 and DP800. The identified FLC based on the proposed method is compared with that of well-established methods such as ISO 12004:2-2008 and time-dependent methods. For both investigated materials, the proposed method presents a lower FLC than the others.

Integrated experimental–numerical investigation of strain partitioning and damage initiation in a low-carbon lath martensitic steel

Lath martensite is a key constituent of advanced high strength steels (AHSS). Its deformation behavior is intrinsically related to its hierarchical structure composed of packets, blocks and laths exhibiting specific topological and orientation relationships. To improve the ductility of lath martensite, it is therefore important not only to clarify the deformation mechanisms but to also gain a better understanding of the damage initiation mechanisms and their connections with local micro-mechanical features. To this end, an integrated experimental–numerical investigation of a low-carbon lath martensitic steel combining large field-of-view high-resolution digital image correlation (HR-DIC) analyses and crystal plasticity (CP) simulations with different modeling assumptions is proposed. The global and local plastic strain field distributions are first comparatively and quantitatively analyzed to clarify the predictive capabilities and limitations of the CP models within the continuum mechanics approximation. The results confirm that plasticity is predominantly carried out by interface sliding so that a model discriminating bulk and boundary elements with respect to their initial in-lath and out-of-lath slip strengths can reasonably reproduce the plastic deformation in terms of spatial distribution and intensity. Severe strain localization is observed along block boundaries with high in-lath Schmid factor, at packet interfaces but also at prior austenite grain boundaries and probably at an annealing twin boundary. The relationship between the strain localization sites and local micro-mechanical fields, in particular the stress triaxiality is discussed.

Modeling and simulation of laser shock waves in elasto-plastic polycrystalline microstructures

We study the propagation of elasto-plastic shockwaves induced by high power laser impacts in 2D polycrystalline metallic alloys in order to investigate the influence of the material microstructure on the fields of plastic strain and subsequent residual stresses. Implementing a visco-plastic constitutive relation at the grain scale accounting for two dislocation slip systems into a finite volume numerical scheme, simulations on single crystal specimens with different lattice orientations show that plastic strain is concentrated in narrow bands originating at the edges of the laser impact and parallel to the slip planes. In the case of polycrystalline microstructures composed of randomly oriented grains, it is found that the microstructure morphology is the origin of a heterogeneous distribution of the residual plastic strain and stress fields, which thus departs from the residual stress fields usually modeled when the microstructure is not accounted for. To account for the random character of polycrystal microstructures, we perform a statistical analysis of the mechanical fields over a large number of microstructures to quantify the dispersion of the results. It is found that even though the residual stresses induced by a laser impact are in compression on average at the center of the laser impact, some realizations of the microstructures can lead to localized concentrations of less compressive, or even tensile, residual stresses at the surface, thus probably reducing the fatigue resistance of the shocked material.

Inverse identification method for determining stress–strain curves of sheet metals at high temperatures

Because of the strong dynamic softening effect of sheet metals at high temperatures, necking occurs early and continues for longer periods. Therefore, obtaining a flow curve after necking has occurred is necessary. The high-temperature flow behavior of materials typically exhibits the coupled effects of work hardening, softening, strain-rate sensitivity, and damage, and using the traditional inverse identification method is quite challenging. This study presents a finite element (FE) inverse identification method that considers work hardening, softening, damage, and strain-rate sensitivity. The method uses a coupled viscoplastic-damage constitutive model as the modified object, and the parameters of the damage equation are iteratively modified by the FE method until the simulated force–displacement curve is consistent with that of the experiment. The identification procedure is demonstrated using 7075 aluminum alloy, and a complete high-temperature flow curve prior to fracture is obtained. The obtained flow curve is applied to analyze the strain field distribution in a hot tensile process and to predict the fracture occurrence and thickness distribution under an isothermal bulging test. Experimental and simulation results are shown to be in good agreement, thus proving the validity of the proposed method.

Crushing behavior and energy absorption of the thousands-of-eyes-Bodhi-inspired novel hierarchical cellular structure

Natural hierarchical materials are proved to have excellent mechanical properties and have been widely applied in the design concept of engineering materials. In this study, inspired by the hierarchical structure of the thousands-of-eyes-Bodhi (TEB), a novel biomimetic hierarchical cellular structure is designed and fabricated using 3D printing technology. The crushing resistance capability and deformation mode of TEB-inspired hierarchical cellular structure are investigated by experiments and simulation methods. Meanwhile the deformation processes are recorded by the compression experiments, and the strain field distributions are analyzed by the digital image correlation (DIC) method. Comparing the mechanical behaviors of square tube, second-order and TEB-inspired hierarchical cellular structures, it is found that the structure hierarchy affects the deformation mode, improves the strain field distribution, delays the strain concentration, and enhances the crashworthiness. It is also noted that the TEB-inspired hierarchical cellular structure exhibits different deformation modes and strain field distributions in the transverse and longitudinal directions, and shows better crushing resistance in the longitudinal direction. In addition, compared with other typical natural materials and engineering materials, the TEB-inspired hierarchical cellular structure possesses superior specific energy absorption and specific strength. These findings provide a new perspective for the application of biomimetic engineering materials.

Experimental and Numerical Studies on Hot Compressive Deformation Behavior of a Cu-Ni-Sn-Mn-Zn Alloy.

Cu-9Ni-6Sn alloys have received widespread attention due to their good mechanical properties and resistance to stress relaxation in the electronic and electrical industries. The hot compression deformation behaviors of the Cu-9Ni-6Sn-0.3Mn-0.2Zn alloy were investigated using the Gleeble-3500 thermal simulator at a temperature range of 700-900 °C and a strain rate range of 0.001-1 s-1. The microstructural evolution of the Cu-9Ni-6Sn alloy during hot compression was studied by means of an optical microscope and a scanning electron microscope. The constitutive equation of hot compression of the alloy was constructed by peak flow stress, and the corresponding 3D hot processing maps were plotted. The results showed that the peak flow stress decreased with the increase in the compression temperature and the decrease in the strain rate. The hot deformation activation energy was calculated as 243.67 kJ/mol by the Arrhenius equation, and the optimum deformation parameters for the alloy were 740-760 °C and 840-900 °C with a strain rate of 0.001~0.01 s-1. According to Deform-3D finite element simulation results, the distribution of the equivalent strain field in the hot deformation samples was inhomogeneous. The alloy was more sensitive to the deformation rate than to the temperature. The simulation results can provide a guideline for the optimization of the microstructure and hot deformation parameters of the Cu-9Ni-6Sn-0.3Mn-0.2Zn alloy.

Multi-side Digital Image Correlation (DIC) evaluation of CFRP bonded to poplar timber

Digital Image Correlation (DIC) is a technique that permits full analysis of the strain field distribution upon the surface of solids. The nonlinear bonding interaction between poplar timber and CFRP (Carbon Fiber Reinforced Polymers) reinforcement under mixed mode I&II is analyzed. The test setup inserts an eccentric axial load and a corresponding bending moment. The experiments show strain distributions composed of two lateral transfer zones in which bonding mode II predominates and, a central zone of constant strain in which bonding mode I is dominant. The maximum load capacity increases with the bond length until the effective bond length.

Tensile Performance Test Research of Hybrid Steel Fiber-Reinforced Self-Compacting Concrete.

Notched beam specimens were loaded by the three-point bending test device, and the effects of different volume contents and combinations of steel fibers on the tensile properties of hybrid steel fiber-reinforced self-compacting concrete (HSFRSCC) were studied. The failure law and strain field distribution of the specimens were studied by digital image correlation (DIC) technology. Moreover, the curves between the load and crack mouth opening displacement (CMOD) of 18 groups of hybrid steel fiber-reinforced concrete specimens were obtained, and the stress-strain curves of 18 groups of specimens were derived from the load-CMOD curves. The results show that both single and hybrid steel fibers can improve the crack deformation resistance and tensile properties of concrete, but hybrid steel fibers have a more significant improvement effect. Only when the content of steel fiber is more than 0.6% can it have a more obvious postpeak descending section, and hybrid steel fiber has higher postpeak deformation capacity and flexural toughness. The fundamental reason why concrete with hybrid steel fibers has better tensile properties is that micro and macro steel fibers cooperate with each other to resist cracks, improving the toughness of concrete after cracking. Finally, the mechanism of different size and volume content of steel fiber was analyzed from the micro level, which can be used as a reference for the engineering design of HSFRSCC in the future.

Finite Element Analysis of Large Plastic Deformation Process of Pure Molybdenum Plate during Hot Rolling

The rare molybdenum resources are being increasingly used in heavy industries. In this study, the common unidirectional and cross hot rolling operations, for pure molybdenum plates, were numerically simulated by using MSC. Marc software. An elastic–plastic finite element model was employed, together with the updated Lagrange method, to predict stress and strain fields in the workpiece. The results showed that there was a typical three-dimensional additional compressive stress (σy> σz > σx) in the deformation zone, while strain could be divided into uniaxial compressive strain and biaxial tensile strain (εy > εx > εz). Tensile stress σx increased with the accumulation of reduction and the decrease in friction coefficient at the edge of the width spread. More importantly, the interlaced deformation caused by cross-commutations, which were helpful in repairing the severe anisotropy created by unidirectional hot rolling. The evolution of the temperature field of pure molybdenum plate was investigated. The surface quenching depth of the pure molybdenum plate was about 1/6 H under different initial temperatures and reductions. In addition, the fundamental reason for the nonuniform distribution of stress and strain fields was the joint influence of rolling stress, contact friction, and external resistance. By comparing the theoretical simulation value of the model with the experimental verification data, we found that the model was aligning well with the actual engineering.

Prediction of strain distribution during the plane strain tensile test based on artificial neural networks

In this study, finite element method was used to study the effects of various notch geometries on the strain field distributions during the plane strain tensile test for cold-rolled steel (DC01). The artificial neural network approach (ANN) and the response surface methodology (RSM) were adopted to develop the mathematical prediction models applied in the optimization procedure. The strain state was expressed by self-defined metrics, namely, the Plane Strain State Index (PSSI) and the Homogeneity Index (HI) were predicted by changing the notch angle (X degree), notch width (d mm), and notch length (c mm). The Quadratic mathematical models obtained by the RSM, and ANN presented the evolution of PSSI, and HI based on (X, d, and c). The results show that the ANN method provides more precise results compared to those of the RSM approach.