Experimental Stress-strain Curves Research Articles

On the strength-ductility modifications in pure copper after severe plastic deformation

The aim of this work is to investigate experimentally and numerically the modifications of both strength and ductility after processing by severe plastic deformation, using several passes of repetitive corrugation and straightening on sheets made of pure copper. Experimental stress–strain curves are determined before and after processing in order to study the influence of the process on the mechanical properties. The modeling of the mechanisms responsible of the mechanical properties evolution is done through the development of an extended Gurson model including a dislocation-based modeling of hardening. The model developed is implemented into a finite element code and applied to the numerical prediction of the repetitive corrugation and straightening followed by a tensile test. The modifications of strength and ductility predicted numerically are qualitatively in good agreement with the experimental observations.

Dynamic mechanical behavior of steel fiber reinforced-recycled aggregate concrete subjected to uniaxial loading

The objective of this study was to investigate the dynamic mechanical performance of steel fiber reinforced-recycled aggregate concrete (SFRAC) under uniaxial loading. A total of 22 groups of cylindrical samples, each measuring 100 mm × 200 mm, were subjected to uniaxial compression. The investigation placed particular emphasis on examining the influence of variables such as the strain rate, volume fraction of steel fiber (Vsf), volume fraction of polyvinyl-alcohol (PVA) fiber (Vpf) and substitution ratio of recycled coarse aggregate (SRCA) on the failure modes, stress-strain curves and deformation ability. The results revealed that the incorporation of steel fibers and PVA fibers enhanced the overall integrity of fractured samples, and induced changes in the failure modes. In particular, the maximum increase in uniaxial compressive strength attributed to strain rate, Vsf and Vpf reached up to 15.0%, 23.57% and 8.57%, respectively. Although the inclusion of recycled aggregates had no significant influence on the failure mode, it decreased the compressive strength by up to 16.34%. Finally, a dynamic stress-strain theoretical constitutive model was established in this paper. The predictions derived from this model closely aligned with the experimental stress-strain curves obtained during the conducted tests. This study provides valuable insights for applications of SFRAC in structural engineering.

Micromechanical modeling for longitudinal tensile property of unidirectional CFRP considering dispersion of fiber properties

Longitudinal tensile failure prediction has always been the focus of research on unidirectional (UD) Carbon Fiber Reinforced Polymer (CFRP). In this paper, the longitudinal tensile tests of unidirectional T800 grade carbon fiber reinforced epoxy resin composite were carried out first. The experimental stress–strain curves show that there are obvious progressive damages before the final failures of the specimens. However, this phenomenon is usually neglected in most of the existing investigations and tests to only obtain elastic modulus and ultimate strength. Thus, a Representative Volume Element (RVE) model based on micromechanics was established using finite element method, considering the randomness of fiber spatial distribution and fiber strength. The tensile strength of fiber monofilaments was assumed to follow a statistical two-parameter Weibull distribution. The failure process of UD composite under longitudinal tensile load was simulated by explicit finite element method. The stress–strain curves obtained by simulation are in good agreement with the experimental results. Finally, the influence of different boundary conditions on the calculation of the RVE was studied. It is found that the final failure strengths of the RVE with uniform displacement boundary conditions are similar to the case of periodic boundary conditions, while the former has higher computational efficiency.

Impact toughness and dynamic constitutive model of geopolymer concrete after water saturation

The dynamic compression test of geopolymer concrete (GC) before and after water saturation was carried out by the split Hopkinson pressure bar (SHPB). And the effects of water saturation and strain rate on impact toughness of GC were studied. Based on Weibull statistical damage distribution theory, the dynamic constitutive model of GC after water saturation was constructed. The results show that the dynamic peak strain and specific energy absorption of GC have strain rate strengthening effect before or after water saturation. The impact toughness of GC decreases after water saturation. The size distribution of GC fragments has fractal characteristics, and the fractal dimension of GC fragments after water saturation is smaller than that before water saturation. The dynamic constitutive model based on Weibull statistical damage distribution theory can accurately describe the impact mechanical behavior of GC after water saturation, and the model fitting curves are in good agreement with the experimental stress–strain curves.

Mechanical impairment characteristics and a novel constitutive model for rocks subjected to uniaxial loading process

The study of constitutive relationship and damage degradation is crucial in solving the stability challenges faced in the rock engineering. In this work, the stress-strain relationships of different type of rocks subjected to uniaxial loading processes are investigated in details. Experimental results demonstrate measurements, such as uniaxial compressive strength (UCS), tangent deformation modulus, peak strain, and Poisson’s ratio ([Formula: see text]). A novel piecewise constitutive model is proposed that utilizes both a constitutive model during compaction and a conventional damage model using the strain equivalence assumption and logistic growth theory to represent the characteristics of stress-deformation curves during both compaction and post-compaction stages. The performance of the proposed constitutive models in capturing deformation characteristics of damaged rocks is demonstrated to be more outstanding in comparison to existing models. In all experimental cases discussed in this study, the proposed model outperforms existing reference models in terms of the coefficients of determination ([Formula: see text]), with the former having coefficients of determination greater than 0.95. Furthermore, physical meanings of relevant model parameters are found to be closely associated with properties of experimental stress-strain curves.

Experimental Construction and Validation of Revised Drucker–Prager Model Using Finite Element Method for Moisture Condensation Zone in Bentonite-Bonded Silica Sand

AbstractFor predicting casting deformation by FEM (finite element method) thermal stress analysis, this paper experimentally constructed and validated the Drucker–Prager (DP) model and its revised model (RDP) for the condensation zone of bentonite-bonded sand molds. The condensation zone has been known as a remarkably low-strength region in the mold, and its mechanical response should be dominant to the casting deformation. To construct the models through uniaxial and triaxial compression tests, the test pieces reproducing the condensation zone were prepared by permeating water vapor through a test piece of bentonite-bonded sand. The constructed models were then applied to the FEM stress analysis of the triaxial test to validate them by comparing the analytical stress–strain curves with the experiment. The experimental stress–strain curve after permeating water did not show any distinct yielding point; however, the analytical curve with the original DP model clearly exhibited a yielding point due to the yield criterion of the model. The distinct yielding criterion should be essentially fatal to reproduce the stress–strain relationship of the condensation zone. Contrarily, the RDP model reproduced the experimental curve with less than 10 % error and was found to be advantageous for modeling the smooth stress–strain relationship of the condensation zone.

Multiscale analysis for characterization of tensile properties in extrusion-based 3D printed carbon nanocomposites

In this study, we proposed a multiscale modeling methodology to predict tensile properties of carbon-based nanocomposites produced through extrusion-based 3D printing. This stepwise method integrates results across scales, from the nanoscale to the macroscale. The stochastic continuum model, informed by molecular dynamics, captures the direction-dependent stiffness of nanocomposites at the atomic level, integrating the transverse isotropic properties and morphological variations, along with process-induced uncertainties in a microscale domain. Considering the variable periodic layered filament shape determined by the printing conditions, we defined the geometry of the representative volume element and derived its homogenized equivalent effective properties. We validated the results of our model by comparing them with experimental stress-strain curves. Using this approach, we simulated the nonlinear response and analyzed the off-axis tensile characteristics of the specimens under various printing conditions. The alignment and orientation of the graphene flakes played pivotal roles in determining the mechanical properties of the nanocomposites. The proposed approach effectively assessed the overall behavior of nanocomposites produced using an extrusion-based 3D printing process, helping to accurately predict the mechanical properties and investigate the effects of the parameters on the macroscopic nonlinear response in applications using 3D printed nanocomposites.

Calculation of the stress-strain state of layers of cross-ply laminate based on an experimental stress-strain curves under uniaxial tension

A method for calculating the stress-strain state of layers of cross-ply laminate based on an experimental deformation diagram under uniaxial tension is proposed. The essence of the method consists in solving a system of two equations describing the experimental curves σx = f(εx) and σx = f(εy), which allows determination of two unknown parameters related to the secant elastic characteristics of the material layers. The law of change in the remaining unknown parameters is set by assumptions regarding deformation of the polymer matrix composite and its layers during loading. To carry out the calculation, it is necessary to set the initial values of the elastic properties of the unidirectional material of the layers, which should be well consistent with the initial values of the elastic properties of the structure under study determined from the experiment. According to the developed algorithm, calculated dependences between average stresses, deformations and secant elastic properties of the layers of the structure are obtained (0°/90°/90°/0°) made of fiberglass E-Glass/MY750 using experimental data from the literature. Calculations carried out for three sets of initial values of the elastic properties of the material under study showed qualitatively identical results. The transverse tensile stress in the 90° layer reaches a maximum in the first half of the stress-strain diagram, and then decreases to zero. A similar stress in the 0° layer reaches a maximum at the failure point of the structure under study. It is revealed that the maximum calculated values of transverse stresses acting in layers 0° and 90° noticeably exceed the transverse tensile strength of the material specified in the literature. The longitudinal tensile stress in the 0° layer reaches a maximum at the failure point and corresponds to 95% of the value of the longitudinal tensile strength of the material. The longitudinal compressive stress in the 90° layer is at a low level throughout the deformation process of the structure under study. The results of this study can be recommended for developing models of the behavior of layers with cracks in the matrix when loading a polymer matrix composite.

Parametric analysis on dilation and confinement of axially loaded circular concrete-filled steel tubes using mesoscale modeling approach

Mesoscale modeling can more realistically describe concrete heterogeneity and phase interaction than macroscopic homogeneous simulation. A mesoscale model was developed in this study to investigate the dilation and confinement behavior of circular concrete-filled steel tube (CFST) columns. The validity of the model was demonstrated by comparing it with experimental stress-strain curves and dilation ratio curves. Parametric analysis revealed that the dilation was non-uniformly distributed along the circumference and the height of the specimen, while an increase in confinement factor inhibited dilation development and promoted confining pressure growth. Based on the parametric analysis, a law for hoop-axial strain relationship and confining pressure versus hoop strain curve were proposed. Additionally, an investigation into the behavior at peak load showed that the dilation ratio of circular CFST at peak load was approximately 0.92. The hoop stress ratio of steel tube decreased from 0.29 to 0.19 as the confinement factor varied from 0.2 to 1.5, while the axial stress showed an opposite growth trend. With increasing confinement factor, confining pressure nonlinearly increased, whereas the load-sharing ratio of between steel tube and concrete showed a linear growth trend. Finally, corresponding formulas were proposed.

Approximation of extracted features enabling 3D design tuning for reproducing the mechanical behaviour of biological soft tissues.

This article describes a new method, inspired by machine learning, to mimic the mechanical behaviour of target biological soft tissues with 3D printed materials. The principle is to optimise the structure of a 3D printed composite consisting of a geometrically tunable fibre embedded in a soft matrix. Physiological features are extracted from experimental stress-strain curves of several biological soft tissues. Then, using a cubic Bézier curve as the composite inner fibre, we optimised its geometric parameters, amplitude and height, to generate a specimen that exhibits a stress-strain curve in accordance with the extracted features of tensile tests. From this first phase, we created a database of specimen geometries that can be used to reproduce a wide variety of biological soft tissues. We applied this process to two soft tissues with very different behaviours: the mandibular periosteum and the calvarial periosteum. The results show that our method can successfully reproduce the mechanical behaviour of these tissues. This highlights the versatility of this approach and demonstrates that it can be extended to mimic various biological soft tissues.

Crystal plasticity simulations with representative volume element of as-build laser powder bed fusion materials

Additive manufacturing of as-build metal materials with laser powder bed fusion typically leads to the formations of various chemical phases and their corresponding microstructure types. Such microstructures have very complex shape and size anisotropic distributions due to the history of the laser heat gradients and scanning patterns. With higher complexity compared to the post-heat-treated materials, the synthetic volume reconstruction of as-build materials for accurate modelling of their mechanical properties is a serious challenge. Here, we present an example of complete workflow pipeline for such nontrivial task. It takes into account the statistical distributions of microstructures: object sizes for each phase, several shape parameters for each microstructure type, and their morphological and crystallographic orientations. In principle, each step in the pipeline, including the parameters in the crystal plasticity model, can be fine-tuned to achieve suitable correspondence between experimental and synthetic microstructures as well as between experimental stress–strain curves and simulated results. To our best knowledge, this work represents an example of the most challenging synthetic volume reconstruction for as-build additive manufacturing materials to date.

Calibration of Micro-Parameters of a Mortar Cylinder Specimen under Simple Compression Using a 2D Discrete Element Model

Masonry systems have been used extensively in historical, commercial, and residential buildings. A large number of experimental and computational studies have been conducted to investigate the behavior of masonry components and systems, including mortar, units (e.g., blocks), and walls. The Discrete Element Method (DEM) has been used to analyze masonry systems with a macro modeling methodology (i.e., structural systems like walls). Masonry systems and their components have not been analyzed using a micro-modeling methodology with the DEM. The objective of this paper is the deterministic calibration of micro-parameters of the mortar cylinder model based on a computationally efficient DEM model. To achieve this objective, a parametric analysis is introduced through a series of models of a mortar specimen tested under simple compression to explore the impact of the model micro-parameters when trying to reproduce a set of experimental observations conducted at the Universidad Autonoma de Yucatan Mexico (UADY). A calibration process based on optimization is implemented to determine the best estimates of the model’s micro-parameters. This paper is divided into three analyses. First, the particle size distribution of the mortar’s aggregate is used as a reference (i.e., scale 1), and then up-scaled 1.5 and two times using four particle sizes; second, using the two-times scaled particle size, the influence of varying particle sizes within a reference particle size distribution was explored (from one particle size to 4 particle sizes following the aggregate particle size distribution); and third, a parametric analysis is performed varying seven micro-parameters, one at the time, varying from 0.25 to 1.5, at 0.25 scale increments, on a model including four particle sizes. The results show micro-parameters and stress-strain curves of mortar for the different analyses, and a representation of the cross sections of the models, indicating the distributions of contact forces. All proposed models showed good agreement with the experimental observations (i.e., stress-strain curve). Also, it was observed from the proposed analyses that some micro-parameters vary as the particle size and the scaled particle size distributions change when using the same experimental stress-strain curve. Also, it was found that the proposed DEM must contain at least two particle sizes to significantly improve the particle interlocking to ensure that the mechanistic behavior reproduces the same experimental observations. Finally, from the results presented in this work, it is concluded that it is possible to produce a computationally efficient model that can later serve as a reference for future research accounting for other control variables such as particle shape, particle size distributions, the exploration of damage propagation effects, and most importantly their corresponding uncertainty quantification and propagation effects in masonry systems.

An experimental-analytical model of elasto-plastic deformation of matrix composites

The experimental-analytical model of nonlinear homogenization of matrix composites is developed on the basis of the Mori-Tanaka secant model. The calculation results of the analytical model are "fitted" to the experimental results. The fitting parameter is the ratio of constrained equivalent strains of the matrices of the experimental sample and the Mori-Tanaka model. Identification of the fitting parameter is performed using the experimental stress-strain curve for the basic composite composition. A linear dependence of the fitting parameter on the volume fraction of particles is used for a composite of arbitrary composition. The calculation results correspond well to the experimental results.

Grain Size Distribution of DP 600 Steel Using Single-Pass Asymmetrical Wedge Test

Grain size distribution after the completion of a phase transformation was studied through the laboratory-controlled hot-plastic deformation of dual phase 600 (DP 600) steel using a specially prepared asymmetric single-pass hot-rolling wedge test with a refined reheating grain size instead of the usual coarse-grained starting microstructure observed in practice. The experiment was performed to reduce generally needed experimental trials to observe the microstructure development at elevated temperatures, where stable and unstable conditions could be observed as in the industrial hot-rolling practice. For this purpose, experimental stress–strain curves and softening behaviors were used concerning FEM simulations to reproduce in situ hot-rolling conditions to interpret the grain size distribution. The presented study revealed that the usual approach found in the literature for microstructure investigation and evolution with a hot-rolling wedge test was deficient concerning the observed field of interest. The degree of potential error concerning the implemented deformation per notch position, as well as the stress–strain rate and related mean flow stresses, were highly related to the geometry of the specimen and the material behavior itself, which could be defined by the actual hardening and softening kinetics (recrystallization and grain growth at elevated temperatures and longer interpass times). The grain size distribution at 1100–1070 °C was observed up to a 3.45 s−1 strain rate and, based on its stable forming behavior according to the FEM simulations and the optimal refined grain size, the optimal deformation was positioned between e = 0.2 and e = 0.5.

New Numerical Method Based on Linear Damage Evolution Law for Predicting Mechanical Properties of TiB2/6061Al.

In order to study the effect of TiB2 particles on the mechanical properties of TiB2/6061Al composites, a series of 3D TiB2/6061Al representative volume elements (RVEs) were established based on SEM photos. This model took into account the ductile damage of the matrix and the traction separation behavior of the interface, and the linear damage evolution law was introduced to characterize stiffness degradation in the matrix elements. Mixed boundary conditions were used in the RVE tensile experiments, and the accuracy of the predicted result was verified by the agreement of the experimental stress-strain curve. The results showed that the addition of TiB2 particles can effectively promote the load-bearing capacity of the composite, but elongation is reduced. When the weight fraction of TiB2 increased from 2.5% to 12.5%, the elastic modulus, yield strength, and tensile strength increased by 8%, 10.37%, and 11.55%, respectively, while the elongation decreased by 10%. The clustering rate of the TiB2 particles is also an important factor affecting the toughness of the composites. With an increase in the clustering rate of TiB2 particles from 20% to 80%, the load-bearing capacity of the composites did not improve, and the elongation of the composites was reduced by 8%. Moreover, the high-strain region provides a path for rapid crack propagation, and particle spacing is a crucial factor that affects the stress field.

A combined experimental and crystal plasticity study of grain size effects in magnesium alloys

This work presents a method to incorporate the micro Hall-Petch equation into the crystal plasticity finite element (CPFE) framework accounting for the microstructural features to understand the coupling between grain size, texture, and loading direction in magnesium alloys. The effect of grain size and texture is accounted for by modifying the slip resistances of individual basal and prismatic systems based on the micro Hall-Petch equation. The modification based on the micro Hall-Petch equation endows every slip system at each microstructural point with a slip system-level grain size and maximum compatibility factor, which are in turn used to modify the slip resistance. While the slip-system level grain size is a measure of the grain size, the maximum compatibility factor encodes the effect of the grain boundary on the slip system resistance modification and is computed based on the Luster-Morris factor. The model is calibrated using experimental stress-strain curves of Mg-4Al samples with three different grain sizes from which the Hall-Petch coefficients are extracted and compared with Hall-Petch coefficients predicted using original parameters from previous work. The predictability of the model is then evaluated for a Mg-4Al sample with different texture and three grain sizes subjected to loading in different directions. The calibrated parameters are then used for some parametric studies to investigate the variation of Hall-Petch slope for different degrees of simulated spread in basal texture, variation of Hall-Petch slope with loading direction relative to basal poles for a microstructure with strong basal texture, and variation of yield strength with change in grain morphology. The proposed approach to incorporate the micro Hall-Petch equation into the CPFE framework provides a foundation to quantitatively model more complicated scenarios of coupling between grain size, texture and loading direction in the plasticity of Mg alloys.

Compressive behaviour of alkali-activated slag-based concrete and Portland cement concrete incorporating novel multiple hooked-end steel fibres

This study investigates the effect of single and multiple hooked-end steel fibres on the mechanical properties of alkali-activated slag-based concrete (AASC) and compares its performance with a similar strength-grade Portland cement concrete (PCC). Three different fibre geometries, i.e. single (Dramix® 3D), double (Dramix® 4D) and triple hooked-end (Dramix® 5D) steel fibres, and three different volume fractions, i.e. 0.25%, 0.50% and 0.75% are considered. Compressive strength, modulus of elasticity and stress–strain response under uniaxial compression are evaluated. Hooked-end steel fibres have a limited effect on the compressive strength and modulus of elasticity of both AASC and PCC, regardless of fibre geometry and content. Although hooked-end steel fibres improve the compressive stress–strain behaviour of both composites, higher enhancement of peak stress, corresponding strain and post-peak response is observed for fibre-reinforced AASC (FRAASC) mixtures. To predict the stress–strain response under uniaxial compression of steel FRAASC a new analytical model is proposed and calibrated using an extensive dataset of experimental stress–strain curves available in the literature for both steel fibre-reinforced PCC and AASC. This model can predict the compressive stress–strain behaviour of FRAASC using the compressive peak stress and corresponding strain of the unreinforced matrix and the steel fibre reinforcing index ({mathrm{RI}}_{mathrm{v}}) as inputs and provides excellent results when validated against the data obtained in this study for FRAASC.

Investigating the Flexural Behavior of a Two-Span High-Performance Concrete Beam Using Experimentally Derived Stress Block Parameters.

High-performance concrete (HPC) is increasingly used in construction due to its superior strength and durability. However, current stress block parameters used for designing normal-strength concrete cannot be safely applied to HPC. To address this issue, new stress block parameters have been proposed through experimental works, which are used for designing HPC members. In this study, the behavior of HPC was investigated using these stress block parameters. Two-span beams made of HPC were tested under five-point bending, and an idealized stress block curve was derived from the experimental stress-strain curve for grades 60, 80, and 100 MPa. Based on the stress block curve, equations for the ultimate moment of resistance, depth of the neutral axis, limiting moment of resistance, and maximum depth of the neutral axis were proposed. An idealized load-deformation curve was also developed, which identified four significant events: first cracking, yielding of reinforced steel, crushing of concrete with spalling of cover, and ultimate failure. The predicted values were found to be in good agreement with the experimental values, and the average location of the first crack was identified to be 0.270 L, measured from the central support on either side of the span. These findings provide important insights for the design of HPC structures, contributing to the development of more resilient and durable infrastructure.

A Semiempirical Model for Post‐Yield Stress Instability in the Stress–Strain Response of 3D Lattice Structures under Compressive Loads

Mechanical behavior of lattice structures is important for a range of engineering applications. Herein, a new semiempirical model is proposed that describes the entire range of stress–strain response of lattice structures, including the stress‐instability region which is modeled as an oscillator. The model can be fit to individual stress–strain curves to extract elastic modulus, yield stress, collapse stress, post‐yield collapse ratio, densification strain, and the energy absorbed per unit volume. The model is fit to 119 unique experimental stress–strain curves from 13 research papers in literature covering four different lattice designs, namely, octet truss, body‐centered cubic with vertical members, body‐centered cubic, and hexagonal. Manufacturing methods (additive and conventional) and materials (metals and polymers) were also included in the analysis. The fitted model yields several new insights into the compression behavior of previously tested lattice structures and can be applied to additional lattice designs. Among other results, analysis of variance (ANOVA) reveals that the octet truss lattice demonstrates the highest post‐yield collapse ratio and the smallest normalized energy absorption per unit volume amongst the lattice structures investigated. The proposed model is a powerful tool for designers to quantitatively compare and select 3D lattice structures with the desired mechanical characteristics.

A simplified prediction method on Chaboche isotropic/kinematic hardening model parameters of structural steels

The Chaboche combined isotropic/kinematic hardening model has gained wide popularity due to its outstanding description on cyclic stress-strain relations of different structural metals. However, the calibration on material parameters of Chaboche model needs to perform at least a cyclic loading test to gain the experimental data, leading to a considerable time and economic cost. To reduce such calibration expense, a simplified calibration approach was proposed in this paper. Firstly, the Chaboche model parameters of various structural steels, including low yield point steels, mild steels, and high strength steels, were calibrated based upon 171 experimental stress-strain curves by using an identical calibration procedure. Secondly, these parameters calibrated were correlated with the monotonic yield strength and fitted through suitable description formulations. Subsequently, a four-steps prediction method of Chaboche model parameters was proposed to replace the traditional complex calibration approach. Based upon the new prediction method, the values of all Chaboche model parameters can be directly obtained when monotonic yield strength is known. Furthermore, the simulation performance of this new prediction method was validated by comparing a series of simulation stress-strain relations with their experimental counterparts. The probabilistic distribution types of these parameters were accordingly identified and the corresponding statistical parameters were fitted. This study provides a simplified prediction method and a probabilistic description on different Chaboche model parameters, producing a foundation for random analysis of stress-strain behaviors on various structural steels.