Uniaxial Stress-strain Response Research Articles

Determination of the Anand Parameters for SAC405 Solders Through the Use of Stress-Strain Data

The Anand inelastic constitutive model is commonly employed to depict the deformation behaviour of solders in electronics components. In the Anand model, plasticity and creep are coupled and described by the same set of flow and evolution relations. Using Anand's constitutive model for SAC405 (95.5Sn-4.0Ag-0.5Cu) lead-free solder, the theoretical equations for the solder's creep reaction and the uniaxial stress-strain response were obtained in this paper. The steps to obtain the parameters of Anand model using stress-strain and creep testing were also determined. Data on uniaxial stress and strain at various temperatures (T = 298 K (25 °C), 323 K (50 °C), 348 K (75 °C), 373 K (100 °C), and 398 K (125 °C)) and strain rates (ε̇ = 1 × 10-3 sec-1, 1 × 10-4 sec-1, and 1 × 10-4 sec-1) was used to calculate the Anand parameters. The Anand model's accurateness (goodness of fit) with the retrieved parameters was assessed by comparing the model's findings to the observed creep and stress-strain data. The Anand model consistently generated good predictions of the empirical data in all cases, across a wide range of temperatures and stress-strain levels. The goodness of fit values obtained were 0.852, 0.835 and 0.902 for strain rate 1 × 10-3 sec-1, 1 × 10-4 sec-1 and 1 × 10-5 sec-1 respectively.

Investigation of grain size and geometrically necessary dislocation density dependence of flow stress in Mg-4Al by using nanoindentation

Models for grain size dependence of flow stress typically ignore contributions from geometrically necessary dislocations (GNDs) in the grain boundary regions. Ashby had proposed the following equation for flow stress (τ) as a function of grain size (d) and effective plastic strain (ε¯): τ=τ0+C′Gbε¯d using an unknown empirical coefficient, C’, In this study, the coefficient, C’, and equation for the grain size dependence of flow stress were investigated in Mg-4Al using nanoindentation. C’ ranges from 1.4 to 7.11 that is related to the hardness difference (∆H0) between the adjacent grains as C′=0.62ΔH0. Ashby equation was used to predict uniaxial stress-strain curves in grain sizes of 55 µm, 187 µm, and 333 µm. The results showed lower flow stress and lower hardening rate compared to experimentally measured tensile stress-strain response. The discrepancy seems to be a result of hardening effect of SSDs. We propose a modified Ashby equation that takes into account the hardening effect of SSDs and GNDs separately, resulting in a better agreement between calculated and experimentally measured values. This analysis demonstrates estimation of uniaxial stress-strain response using nanoindentation measurements that captures effects of grain size, and strain hardening from SSDs and GNDs. The combination of the revised equation and nanoindentation method will enable rapid exploration of stress-strain response of a diverse range of single-phase polycrystalline alloys.

Global and Local Deformation Analysis of Mg-SiC Nanocomposites: Digital Image Correlation (DIC) and Representative Volume Element (RVE) Techniques

Improving the ductile deformation behavior of Mg-SiC nanocomposites without compromising strength is critical to enhancing their mechanical properties. Mg-SiC nanocomposites are produced through mechanical milling, cold isostatic pressing, sintering, and hot extrusion processes. This study investigates the uniaxial stress–strain response and deformation behavior of the Mg-SiC nanocomposite compared to pure Mg samples with and without the milling process. The deformation behavior was investigated by two-dimensional (2D) digital image correlation (DIC) at two macroscopic and microscopic scales, employing light micrographs and in situ loading samples, respectively, in the scanning electron microscope. Compared to the pure Mg samples, the mechanical test results demonstrated a significant improvement in strength (80 MPa) and fracture strain (23.5%) of the Mg-SiC nanocomposite. The three-dimensional (3D) representative volume element (RVE) model revealed the particle dispersion effect on the mechanical properties of the nanocomposite. The RVE results demonstrate ductile deformation behavior in the sample with homogenous dispersion of SiC particles compared with the heterogeneous dispersion of SiC particles in Mg-SiC nanocomposite. The results demonstrated a good agreement between DIC and RVE predictions for Mg-SiC nanocomposites across macro- and microscales.

3D mesoscale modelling of recycled aggregate concrete

Mesoscale modelling is a promising tool to analyse the phenomenological causes of mechanical failure of recycled aggregate concrete (RAC). Most mesoscale models of RAC are two-dimensional (2D) and 3D models are lacking. This prevents the full understanding of the behaviour of each mesoscopic phase. This paper presents a 3D model of RAC and analyses its mechanical behaviour based on mesoscale phenomena. The analyses concern three types of tests carried out in concrete specimens: uniaxial compressive, uniaxial tensile and splitting tensile strength tests. The mechanical response and fracture behaviour of each mesoscopic phase is analysed in relation to the response of RAC specimen. The comparisons between uniaxial behaviour of 3D and 2D modelling as well as between uniaxial and splitting tensile behaviour of RAC are presented. The main findings of the paper are: (1) the full curve of uniaxial stress-strain response from 3D modelling is comparable to that from 2D modelling for RAC (therefore, 2D models are validated for RAC modelling); (2) the overall behaviour of the concrete elements remains elastic regardless of the fracture development in the ITZ and attached mortar of recycled aggregates until damage propagates to the new mortar matrix; (3) a relationship between modelled uniaxial and splitting strength of RAC is established and validated.

Study on correlation and scaling protocol between indentation stress-strain and uniaxial stress-strain

Most important mechanical structures produce complex local material changes during the moulding and servicing process. Obtaining the specific local mechanical properties of materials and conducting field tests are problems in structural integrity evaluation. The instrumented indentation technique (IIT) is a solution to these problems. However, the core challenge with the IIT is the quantitative correlation between indentation response and uniaxial stress-strain (USS) response. In this study, we investigate the scaling relationship between indentation stress-strain (ISS) and uniaxial stress-strain (USS). A new protocol for obtaining the mechanical properties of alloy steels using ISS curves is proposed, which can directly obtain the plastic stage of the USS curves from the ISS curves. We used a finite element inversion method based on existing theories. Models with different mechanical properties (USS curves) were established using the ABAQUS software to obtain the corresponding ISS curves. We then explored the relationship between the two; the strain-scaling factor and stress-scaling function were specifically identified. Our work proposes an ISS protocol for power-law-hardening materials. Two alloy steels (SA508 and 42CrMo) were experimentally verifieds. The predicted results are approximately consistent with the practical curves and the error was within ± 10%. Because of the universality and reliability of the protocols, it is expected to provide a theoretical reference and technical approach for the development of IITs and structural integrity evaluation of important mechanical structures.

A Macromechanical Constitutive Model for Rebar Buckling

Rebar buckling and fracture have been experimentally observed to cause significant degradation of the mechanical properties of reinforced concrete (RC) elements and should be accounted for in the analysis of RC structures. While data on the material properties of steel rebar are widely available, test data on rebar buckling remain scarce. This paper proposes a macromechanical model capable of predicting rebar buckling responses solely on the basis of steel material properties and the rebar geometry, even when rebar buckling experimental data are not available. This is achieved by computationally building the uniaxial stress-strain constitutive response at each analysis step through the equilibrium in the deformed configuration of the buckled rebar and through the cross-sectional constitutive response. The equilibrium in the deformed configuration is treated in a manner consistent with the corotational formulation, while the cross-sectional constitutive response is built through integration of a uniaxial damage plasticity model over the cross-section area. Rebar buckling is triggered by an initial imperfection, while low-cycle fatigue effects are reproduced through the uniaxial damage plasticity steel material model, without the need for cycle-counting algorithms. The proposed model is translated to a computer code, calibrated to a set of experimental data, validated to separate test data, and subsequently used in the analysis of an experimentally studied RC column that experienced rebar buckling under cyclic loading. Using the proposed model, the analysis captured the response of the RC column and the experimentally observed strength deterioration due to rebar buckling.

High strength and ductility in a heterostructured nanotwinned Ni film

We report the synthesis and mechanical behavior of two nanotwinned (NT) Ni films with different distributions of twin widths along the film growth direction. The NT Ni films, deposited on Si (111) substrates with an Ag buffer layer, are composed of two crystallographic variants with (111) out-of-plane orientation, which results in the formation of twin boundaries at their interfaces. The uniaxial stress-strain response of the freestanding NT Ni films was measured using MEMS tensile testing stages. While both films exhibited high strength, the film with a larger mean and broader distribution of twin widths exhibited significant strain hardening as well, which led to uniform elongation of ∼10%. These results suggest that by controlling the twin width distribution it is possible to realize a synergistic combination of strength and ductility in NT metal films.

Microscale damage evolutions in fiber-reinforced composites with different initial defects

In this study, an effective microscale model for fiber-reinforced composites with initial damages is presented to investigate local stress distribution and damage evolution at constitutive material level. To validate the proposed numerical model, experimental data of uniaxial stress–strain responses and off-axis failure strength are employed for a comparison, and a good agreement by comparing with numerical results can be found. To represent the microscale damage evolution in the representative volume element, stiffness degradation coefficients are subtly applied to describe the failure sub-cells. Moreover, microscale damage evolutions and local stress distribution in the composites subjected to uniaxial and biaxial loads are both investigated. The effect of three different modes of initial damage in the composites are studied. The influences of the distribution, location and orientation of initial damage on damage evolutions are also studied.

Characterization of plastically compressible solids via spherical indentation

The response in spherical indentation is used to identify material properties for plastically compressible materials with presumed known elastic properties. The materials are assumed to be characterized by a Deshpande–Fleck constitutive relation (Deshpande and Fleck, 2000). The indentation force versus indentation depth responses and the residual surface profiles (the surface profiles after unloading) are calculated for two sets of material parameters. These are regarded as the “experimental” input materials. The constitutive parameters for these two materials are identified using the Bayesian-type statistical approach of Zhang et al. (2019) both for noise-free and for noise-contaminated data. The uniaxial stress–strain responses obtained from the spherical indentation responses are good approximations of those of the “experimental” input materials, particularly if surface profile data is used, but the quality of the approximation decreases with increasing noise amplitude. Plastic compressibility is found to have a relatively small effect on the correction factor β in the Oliver–Pharr relation (Oliver and Pharr, 2004) between the unloading slope and the effective (or reduced) elastic modulus. The indentation response of the plastically compressible materials can be well-represented by a nearly incompressible plastic constitutive relation but the inferred uniaxial stress–strain response is a poor representation of the “experimental” material uniaxial stress–strain response. The predicted residual surface profile is less dependent on the assumed elastic constant values than is the indentation force versus indentation depth response. The indentation force versus indentation depth responses in spherical indentation for three materials with very different uniaxial stress–strain curves are found to be indistinguishable if the indentation depth is sufficiently small but are distinguishable if the indentation depth is sufficiently large.

Correlation of Measured Load-Displacement Curves in Small Punch Tests with Tensile Stress-Strain Curves

The Small Punch Test (SPT) has demonstrated tremendous potential for high throughput evaluation of mechanical response of metal sheets. However, its application has thus far been limited to the estimation of plastic material properties such as yield strength and ultimate tensile strength. This paper demonstrates new analysis protocols for extracting the uniaxial stress-strain curves from the SPT measured load-displacement curves. This is accomplished by first establishing a correlation between the SPT measurements and corresponding finite element (FE) simulations that take as input the uniaxial stress-strain response of the material. After establishing this correlation, it is shown that the correlation can be inverted to estimate the uniaxial stress-strain response from the SPT load-displacement measurement on a new material sample.

Inverse Method to Determine Fatigue Properties of Materials by Combining Cyclic Indentation and Numerical Simulation

The application of instrumented indentation to assess material properties like Young’s modulus and microhardness has become a standard method. In recent developments, indentation experiments and simulations have been combined to inverse methods, from which further material parameters such as yield strength, work hardening rate, and tensile strength can be determined. In this work, an inverse method is introduced by which material parameters for cyclic plasticity, i.e., kinematic hardening parameters, can be determined. To accomplish this, cyclic Vickers indentation experiments are combined with finite element simulations of the indentation with unknown material properties, which are then determined by inverse analysis. To validate the proposed method, these parameters are subsequently applied to predict the uniaxial stress–strain response of a material with success. The method has been validated successfully for a quenched and tempered martensitic steel and for technically pure copper, where an excellent agreement between measured and predicted cyclic stress–strain curves has been achieved. Hence, the proposed inverse method based on cyclic nanoindentation, as a quasi-nondestructive method, could complement or even substitute the resource-intensive conventional fatigue testing in the future for some applications.

On the potential of recurrent neural networks for modeling path dependent plasticity

The mathematical description of elastoplasticity is a highly complex problem due to the possible change from elastic to elasto-plastic behavior (and vice-versa) as a function of the loading path. Advanced physics-based plasticity models usually feature numerous internal variables (often of tensorial nature) along with a set of evolution equations and complementary conditions. In the present work, an attempt is made to come up with a machine-learning based model that can replicate the predictions anisotropic Yld2000-2d model with homogeneous anisotropic hardening (HAH). For this, a series of modeling problems of increasing complexity is formulated and sequentially addressed using neural network models. It is demonstrated that basic fully-connected neural network models can capture the characteristic non-linearities in the uniaxial stress-strain response such as the Bauschinger effect, permanent softening or latent hardening. A neural network with gated recurrent units (GRUs) and fully-connected layer is proposed for the modeling of plane stress plasticity for arbitrary loading paths. After training and testing the model through comparison with the Yld2000-2d/HAH model, the recurrent neural network model is also used to model the multi-axial stress-strain response of a two-dimensional foam. Here, the comparison with the results from unit cell simulations provided another validation of the proposed data-driven modeling approach.

An Explicit, Accurate Approach Toward Modeling Irrecoverable Deformation Effects of Shape Memory Alloys

Finite strain plastic deformation effects of SMAs are simulated based on finite strain elastoplastic J2-flow equations, in a direct sense with no reference to any additional variables for phase transition mechanisms. Uniaxial loading-unloading curves of any given shape may be exactly reproduced as uniaxial stress-strain responses of these equations in each loading-unloading cycle. A new technique for combining linear spline functions into a unified, smooth interpolating function is proposed toward the purpose of explicitly, accurately fitting any given test data for both loading and unloading cases.

Influence of Assumed Strain Hardening Relation on Plastic Stress-Strain Response Identification From Conical Indentation

Abstract Instrumented indentation tests provide an attractive means for obtaining data to characterize the plastic response of engineering materials. One difficulty in doing this is that the relation between the measured indentation force versus indentation depth response and the plastic stress-strain response is not unique. Materials with very different uniaxial stress-strain curves can give essentially identical curves of indentation force versus indentation depth. Zhang et al. (2019, “Identification of Plastic Properties From Conical Indentation Using a Bayesian-Type Statistical Approach,” ASME J. Appl. Mech., 86, p. 011002) numerically generated “experimental” conical indentation data and showed that using surface profile data and indentation force versus indentation depth data together with a Bayesian-type statistical analysis permitted the uniaxial plastic stress-strain response to be identified even for materials with indistinguishable indentation force versus indentation depth curves. The same form of hardening relation was used in the identification process as was used to generate the “experimental” data. Generally, a variety of power law expressions have been used to characterize the uniaxial plastic stress-strain response of engineering materials, and, of course, the form that gives the best fit for a material is not known a priori. Here, we use the same Bayesian statistics-based analysis but consider four characterizations of the plastic uniaxial stress-strain response and show that the identification of the hardening relation parameters and the associated uniaxial stress-strain response is not very sensitive to the form of the power law strain hardening relation chosen even with data that have significant noise.

Uniaxial Tensile Stress-Strain Response on the 3D Angle Interlock Woven Fabric Composite

An experimental study have been performed to investigate the uniaxial tensile stress-strain response on the 3D angle interlock (3DAI) woven fabric composite. The tensile analysis were examined based on different woven fabric set-up parameter of draw-in plan ; pointed (DRW 1), broken (DRW 2), broken mirror (DRW 3), and straight (DRW 4). Meanwhile, the woven fabric composite were produced based on 22 and 25 pick.cm-1 of weft densities. The outcomes produced shown that woven composite sample with 25 pick.cm-1 on DRW 4 projected the highest stress response, 113 MPa. Extensive review indicated that DRW 1 and 4 gave better tensile stress-strain response than the other counterpart.

Modelling the performance of devices based on thin dielectric elastomer membranes

Actuators based on thin dielectric elastomer (DE) membranes with very low modulus, high dielectric permittivity and dielectric breakdown strength have recently been used in a number of diverse applications. In order to be technologically viable, the fidelity of their responses, especially in operations over large number of cycles, and failure mechanisms need to be understood and modelled. We present a simple, uncoupled, explicit scheme for simulating actuators based on DE membranes that depends on a characterisation of the material as a electro-visco-hyperelastic one. Experimental charactersiation of the uniaxial viscoelastic stress strain response, stretch dependent dielectric permittivity and breakdown strength of a commonly used DE material has been carried out. The simulation methodology has been verified against the performance of a circular membrane based actuator subjected to a cyclic potential. The simulations reproduced the experimental responses well and also allowed us to computationally map out the parameter space for safe operation of the actuator.

A computational mechanics engineering framework for predicting the axial crush response of Aluminum extrusions

Automakers are developing new lightweight aluminum alloys for automotive structures to reduce vehicle weight. However, these alloys require extensive mechanical characterization for accurate calibration of a numerical model, which is often a painstaking task. Automakers are exploring alternative strategies to reduce the number of experiments required for characterizing these new alloys without sacrificing accuracy in predicting performance. The method of virtual experimentation through computational mechanics engineering (CME) with crystal plasticity is showing promise in satisfying this need. This work presents a CME framework for predicting the axial crush behavior of an aluminum alloy AA6060-T6 extrusion using only a single uniaxial stress-strain response and 2D electron backscatter diffraction (EBSD) scans. An anisotropic phenomenological model is generated using a 3D reconstructed microstructure and a calibrated crystal plasticity model. Additional mechanical characterization is performed to qualify the proposed CME framework. Finite element simulations that employ the CME framework are performed to evaluate the suitability of this methodology in quasi-static axial crush applications. Quasi-static axial crush experiments of the extrusion are performed to validate the finite element simulations and the CME framework. Simulations using the CME framework were capable of predicting the experimental crush response with 3–4%. The proposed CME framework can help automakers reduce the number of experiments needed for the development of components in large deformation, such as crush.

Uniaxial fatigue, creep and stress-strain responses of steel 30CrNiMo8

The choice of individual material for industrial application is primarily based on knowledge of its behavior in similar applications and similar environmental conditions. Contemporary design implies knowledge of material behavior and knowledge in the area of structural analysis supported by large capacity computers. Bearing this in mind, this paper presents and analyzes the experimental results related to the mechanical properties of the material considered (30CrNiMo8/1.6580/AISI 4340) at different temperatures as well as its creep and fatigue behavior. All experimental tests were carried out as uniaxial tests. The test results related to the mechanical properties are presented in the form of engineering stress-strain diagrams. The results related to the creep behavior of the material are shown in the form of creep curves, while the fatigue of the material is shown in the form of stress – life (S – N) diagram. Based on these experimental results, the values of the following properties are determined: ultimate tensile strength (σm, 20 = 696 MPa), yield strength (σ0.2, 20 = 355.5 MPa), modulus of elasticity (E, 20 = 217 GPa) and fatigue limit (σf, 20, R = 280.4 MPa). Results related to fatigue tests were obtained at room temperature and stress ratio R = -1.

Microstructure and mechanical behaviour of additive manufactured Ti–6Al–4V parts under tension

Metal-based additive manufacturing technologies using electron or laser beams as a heat source for melting a metal powder or wire have been the subject of keen interest in recent years. At present paper a comparative analysis of the microstructure, strain response during tensile test and mechanical properties of Ti–6Al–4V samples produced by selective laser melting, electron beam melting or electron beam free-form fabrication were performed. A microstructural study using transmission electron microscopy revealed columnar prior β grains transformed into a lamellar α-morphology in the samples. According to X-ray diffraction study, the volume fractions of the β-Ti phase in the samples were equal to 2, 4 and 6 % respectively. It has been shown that the Vickers microhardness of SLM and EBM Ti–6Al–4V samples was similar (~5.4 GPa) while the hardness of EBF3 parts was significantly lower (4.5 GPa). The uniaxial stress-strain response of the Ti–6Al–4V samples fabricated by different additive manufacturing technologies were compared. Crystallographic (dislocation motion) and non-crystallographic (shear banding) deformation mechanisms of the loaded samples were studied by scanning electron microscopy and optical profilometry.

Identification of Plastic Properties From Conical Indentation Using a Bayesian-Type Statistical Approach

The plastic properties that characterize the uniaxial stress–strain response of a plastically isotropic material are not uniquely related to the indentation force versus indentation depth response. We consider results for three sets of plastic material properties that give rise to essentially identical curves of indentation force versus indentation depth in conical indentation. The corresponding surface profiles after unloading are also calculated. These computed results are regarded as the “experimental” data. A simplified Bayesian-type statistical approach is used to identify the values of flow strength and strain hardening exponent for each of the three sets of material parameters. The effect of fluctuations (“noise”) superposed on the “experimental” data is also considered. We build the database for the Bayesian-type analysis using finite element calculations for a relatively coarse set of parameter values and use interpolation to refine the database. A good estimate of the uniaxial stress–strain response is obtained for each material both in the absence of fluctuations and in the presence of sufficiently small fluctuations. Since the indentation force versus indentation depth response for the three materials is nearly identical, the predicted uniaxial stress–strain response obtained using only surface profile data differs little from what is obtained using both indentation force versus indentation depth and surface profile data. The sensitivity of the representation of the predicted uniaxial stress–strain response to fluctuations increases with increasing strain hardening. We also explore the sensitivity of the predictions to the degree of database refinement.