Multiscale prediction of mechanical behavior of ferrite–pearlite steel with numerical material testing

Multiscale mechanical behaviors of ferrite–pearlite steel were predicted using numerical material testing (NMT) based on the finite element method. The microstructure of ferrite–pearlite steel is regarded as a two‐component aggregate of ferrite crystal grains and pearlite colonies. In NMT, the macroscopic stress–strain curve and the deformation state of the microstructure were examined by means of a two‐scale finite element analysis method based on the framework of the mathematical homogenization theory. The microstructure of ferrite–pearlite steel was modeled with finite elements, and constitutive models for ferrite crystal grains and pearlite colonies were prepared to describe their anisotropic mechanical behavior at the microscale level. While the anisotropic linear elasticity and the single crystal plasticity based on representative characteristic length have been employed for the ferrite crystal grains, the constitutive model of a pearlite colony was newly developed in this study. For that reason, the constitutive behavior of the pearlite colony was investigated using NMT on a smaller scale than the scale of the ferrite–pearlite microstructure, with the microstructure of the pearlite colony modeled as a lamellar structure of ferrite and cementite phases with finite elements. On the basis of the numerical results, the anisotropic constitutive model of the pearlite colony was formulated based on the normal vector of the lamella. The components of the anisotropic elasticity were estimated with NMT based on the finite element method, where the elasticity of the cementite phase was numerically evaluated with a first‐principles calculation. Also, an anisotropic plastic constitutive model for the pearlite colony was formulated with two‐surface plasticity consisting of yield functions for the interlamellar shear mode and yielding of the overall lamellar structure. After addressing the microscopic modeling of ferrite–pearlite steel, NMT was performed with the finite element models of the ferrite–pearlite microstructure and with the microscopic constitutive models for each of the components. Finally, the results were compared with the corresponding experimental results on both the macroscopic response and the microscopic deformation state to ascertain the validity of the numerical modeling. Copyright © 2011 John Wiley & Sons, Ltd.     

Approximate local elasto-plastic solution for notched plates undergoing cyclic tensile loading

This work presents a simple methodology to estimate the inelastic stress and strain histories at the root of the notch of a thin elasto-plastic plate undergoing any complex non-monotonic tensile loading. It is proposed an extension of the classical Neuber and Linear projection rules to the case of non-monotonic loading. Using such extended projection techniques, the stress–strain curve at the root of the notch is similar to the curve obtained in a non-monotonic tensile test with prescribed strain. In this test, the limit strain at each reversal depends on the loading history and on the adopted projection technique, what is very important mainly if cyclic hardening (or softening) occurs. The basic idea is to replace this experimental curve by a numerically generated one. A very easy to implement algorithm is proposed to automatically generate the stress–strain curve and to perform the projection. A constitutive theory that accounts for the hardening effects induced by cyclic plasticity is considered. A simple procedure to identify all the material constants that arise in this theory from only one cyclic tensile test with controlled deformation is also presented. Examples concerning cyclic loading in notched aluminium plates are presented to show the main features of the proposed methodology.     

Elastic-plastic stress-strain calculation in notched bodies subjected to non-proportional loading

An analytical method for calculating notch tip stresses and strains in elastic-plastic isotropic bodies subjected to non-proportional loading sequences is presented. The key elements of the two proposed models are generalized relationships between elastic and elastic-plastic strain energy densities, and the material constitutive relations. These two models form the lower and the upper limits of the actual energy densities at the notch tip. Each method consists of a set of seven linear algebraic relations that can easily be solved for elastic-plastic strain and stress increments, knowing the hypothetical notch tip elastic stress history and the material stress-strain curve. Results of the validation show that the proposed methods compare well with finite element data and each solution set forms the limits of a band within which actual notch tip strains fall.     

A Combined Analytic,Numeric, and Experimental Investigation Performed on NiTi/NiTiCu Bi‐Layer Composites under Tensile Loading

Adjusting mechanical behavior and controlling deformation parameters are significant tasks in designing shape memory components. In this paper, an analytical model describes the deformation behavior of NiTi/NiTiCu bi‐layer composites under tensile loading. Different deformation stages are considered based on single mechanical behavior at each stage. Closed‐form equations are derived for stress–strain variations of bi‐layer composites under uniaxial loading–unloading. Bi‐layer composites made via the diffusion bonding method from single layers of NiTi alloy with a composition of Ti‐50.7 at.% Ni, as an austenitic layer, and Ti‐45 at% Ni‐5 at% Cu, as a martensitic layer, are produced by the vacuum arc remelting technique. The tensile behavior of single‐ and bi‐layers is investigated by using loading–unloading experiments to find the nominal stress–strain curves. Numerical simulations are also done by employing Lagoudas constitutive model to simulate stress–strain diagrams. The solutions of the analytical method presented are validated by using the numerical simulations as well as the experimental results. With regard to the results obtained from the analytical modeling, the numerical simulations, and the experiments, it is evident that the bi‐layer composites with different thickness ratios provide adjustable mechanical behavior that can be considered in different application designs, for example, actuators equipped with shape memory components.

     

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are investigated.     

Anisotropic behavior of superelastic NiTi shape memory alloys; an experimental investigation and constitutive modeling

The effect of boundary condition on the mechanical behavior of superelastic NiTi shape memory alloys is investigated in this paper. Experimental tests were carried out on NiTi tubes subjected to tension and torsion with different boundary conditions including fixed and free end cases. Results revealed that anisotropy strain/stress appears in the material depending on the end boundary condition of the sample when martensite transformation occurs. This phenomenon is believed to be a result of anisotropy developed in NiTi during material processing and/or training procedures. Based on experimental findings, a new extension is considered to a 3-D phenomenological constitutive model to capture the anisotropic transformation strain/stress generation observed during different loading conditions. Numerical correlations between predicted and experimental data demonstrate the success of the modified model.     

Analytical evaluation on uniaxial tensile deformation behavior of fiber metal laminate based on SRPP and its experimental confirmation

Uniaxial tensile tests have been carried out to accurately evaluate the in-plain mechanical properties of fiber metal laminates (FMLs). The FMLs in this paper comprised of a layer of self-reinforced polypropylene (SRPP) sandwiched between two layers of aluminum alloy 5052-H34. In this study, nonlinear tensile and fracture behavior of FMLs under in-plane loading conditions has been investigated with numerical simulations and theoretical analysis. The numerical simulation based on finite element modeling using the ABAQUS/Explicit and the theoretical constitutive model based on the volume fraction approach using the rule of mixture and the modified classical lamination theory, which incorporates the elastic–plastic behavior of the aluminum alloy and SRPP, are used to predict the in-plain mechanical properties such as stress–strain response and deformation behavior of the FMLs. In addition, the pre-stretching process is used to reduce the thermal residual stresses before the uniaxial tensile tests of the FMLs. Through comparing the numerical simulations and the theoretical analysis with the experimental results, it is concluded that the adopted numerical simulation model and the theoretical approach can describe with sufficient accuracy of the actual tensile stress–strain curve.     

The effect of grain orientation on the tensile‐compressive asymmetry of polycrystalline NiTi shape memory alloy

The purpose of the present study is to thoroughly understand the influence of crystallographic texture on the stress‐strain asymmetric behavior of polycrystalline NiTi shape memory alloy under tension and compression. To do this, a 3D thermo‐mechanical model has been implemented in a finite element program and textured and untextured polycrystalline NiTi have been considered. In our polycrystalline finite element model, each element represents one grain and a set of crystal orientations which approximate the initial crystallographic texture of the NiTi are assigned to the elements. From the calculated results, it is found that the crystallographic texture is the important reason for the tension‐compression asymmetry. For the textured polycrystal, the tension‐compression asymmetry can be observed clearly, but for the polycrystal containing randomly oriented grains, the stress‐strain curves show low levers of asymmetry between tensile and compressive loading, and the evolutions of martensite volume fractions are similar under two stress states.     

Modeling of Nonlinear Mechanical Behavior for 3D Needled C/C-SiC Composites Under Tensile Load

This paper established a macroscopic constitutive model to describe the nonlinear stress–strain behavior of 3D needled C/C-SiC composites under tensile load. Extensive on- and off-axis tensile tests were performed to investigate the macroscopic mechanical behavior and damage characteristics of the composites. The nonlinear mechanical behavior of the material was mainly induced by matrix tensile cracking and fiber/matrix debonding. Permanent deformations and secant modulus degradation were observed in cyclic loading-unloading tests. The nonlinear stress–strain relationship of the material could be described macroscopically by plasticity deformation and stiffness degradation. In the proposed model, we employed a plasticity theory with associated plastic flow rule to describe the evolution of plastic strains. A novel damage variable was also introduced to characterize the stiffness degradation of the material. The damage evolution law was derived from the statistical distribution of material strength. Parameters of the proposed model can be determined from off-axis tensile tests. Stress–strain curves predicted by this model showed reasonable agreement with experimental results.     

A notch strain calculation of a notched specimen under axial-torsion loadings

In this paper, a notch analysis model is presented for the numerical prediction of multiaxial strains of a notched 1070 steel specimen under combined axial and torsion loadings. The proposed model is based on the notion of a structural yield surface and uses a small-strain cyclic plasticity model to describe stress–strain relations. A notch load–strain curve is calculated with Neuber’s rule and incremental nonlinear finite element analysis. The presented model is applied to simulate the notch root deformations of a circumferentially notched specimen under cyclic tension–compression–torsion loading histories. The model predictions are evaluated with strain measurements at the notch root of the specimen in a comprehensive set of cyclic tests. The computed strain loops were in accord with experimental data and matched qualitatively with measured shear–axial strain histories irrespective of loading path of the test. In proportional balanced torsion-axial loading, the nonlinear shear strain–axial strain loops were calculated properly. The modeling errors were determined to be a function of the loading path shape, and compared to shear strains, axial strain predictions were more accurate.     

A comparative study of dynamic, ductile fracture initiation in two specimen configurations

In this work a single edge notched plate (SEN(T)) subjected to a tensile stress pulse is analysed, using a 2D plane strain dynamic finite element procedure. The interaction of the notch with a pre-nucleated hole ahead of it is examined. The background material is modelled by the Gurson constitutive law and ductile failure by microvoid coalescence in the ligament connecting the notch and the hole is simulated. Both rate independent and rate dependent material behaviour is considered. The notch tip region is subjected to a range of loading rates J by varying the peak value and the rise time of the applied stress pulse. The results obtained from these simulations are compared with a three point bend (TPB) specimen subjected to impact loading analysed in an earlier work [3]. The variation of J at fracture initiation, J _c, with average loading rate J is obtained from the finite element simulations. It is found that the functional relationship between J _c and J is fairly independent of the specimen geometry and is only dependent on material behaviour.     

A study on micro-mechanical deformation behaviour of heat-treated 20MnMoNi55 steel

Several heat treatment procedures are designed considering critical temperatures of phase transformation evaluated through dilatometric testing of 20MnMoNi55 steel to transform low carbon bainitic as-received material into ferrite-martensite dual-phase steels consisting of varied martensite fractions. A thorough metallographic study correlated with the micro-hardness of constituent phases ensures morphological characteristics along with its fractional variations in as-received and dual-phase steels. The impact of fractional variation in constituent phases on the uniaxial monotonic deformation characteristics of dual-phase steels has been observed with a correlation study between experimental tensile and finite element simulated results. Therefore, a physical-based model with a 2-dimensional representative volume element has been established, addressing actual morphological characteristics obtained from metallographic studies. Moreover, the constitutive flow behaviours of ferrite and martensite are also derived from the dislocation-based hardening model to address the actual deformation phenomenon. Finally, an inhomogeneous deformation behaviour among constituent phases and localization of plastic strain in ferrite matrix has been observed with von-Mises stress, and equivalent plastic strain distribution through finite element simulated results. This phenomenon is again confirmed with kernel average misorientation mapping and geometrically necessary dislocation density evaluation through electron backscattered diffraction of tensile samples subjected to different degrees of plastic strain.     

Effect of martensite transformation on fracture behavior of shape memory alloy NiTi in a notched specimen

In this paper, the finite element calculation of the stress–strain distribution in front of a notch tip were carried out for two materials. One is a shape memory alloy NiTi with the stress-induced martensite transformation, and another is a fully transformed martensite NiTi without the transformation. Based on the results obtained, and combining a model of the fracture process zone, effect of martensite transformation on the fracture behavior of the shape memory alloy NiTi in a notched specimen of plane stress state is comparably analyzed. The results show that the martensite transformation increases the load to produce plastic deformation in the transformed martensite at the notch tip and decreases the maximum normal stress and plastic strain near the notch tip, and tends to suspend the crack nucleation and propagation in the fully transformed martensite in front of the notch tip, and thus increases the fracture load and improves the toughness. A quantitative analysis based on the model of the fracture process zone shows that the martensite transformation in the SMA NiTi causes about 47% increase in the apparent fracture toughness.     

Predictive modelling of the properties and toughness of polymeric materials Part I Why is polystyrene brittle and polycarbonate tough?

The brittleness of polystyrene (PS) and the toughness but notch sensitivity of polycarbonate (PC) have been studied by the detailed finite element analyses of the stress and strain fields in a notched tensile bar with a minor defect. The defect represented a flaw or imperfection, generated during the test specimen production. The large-strain mechanical responses of both materials were approximated by an accurate elasto-viscoplastic constitutive model with appropriate material parameters. It was assumed that failure occurs instantaneously once the dilative stress exceeds a certain critical craze-initiation stress. The analyses show that the unstable post-yield mechanical response of both materials results in localisation of stresses and strains near the defect at a very low macroscopic strain (0.16%). As a result, a strong dilative stress concentration is formed just below the surface of the defect. For the polystyrene specimen, the critical stress is reached at the defect. For the polycarbonate, however, the effect of the stress concentrating defect was counteracted by a higher craze-initiation stress and stronger strain hardening. The PC craze-initiation resistance, however, did not suffice to overcome the dilative stress concentration raised by the notch tip.     

Finite element implementation of a kinetic model of dynamic strain aging in aluminum–magnesium alloys

Soare and Curtin (Acta Mater. 2008; 56 :4091–4101, 4046–4061) have recently developed a model of dynamic strain aging in solute‐strengthened alloys. Their constitutive law describes time‐dependent solute strengthening using rate equations that can be calibrated using atomistic simulations. In this paper, their material model is incorporated into a continuum finite element simulation, with a view to completing a multi‐scale method for predicting the formability of solute‐strengthened alloys. The Soare–Curtin model is first re‐formulated as a state‐variable constitutive law, which is suitable for finite element computations. An efficient numerical procedure is then developed to track the strength distribution of aging mobile and forest dislocations in the solid during deformation. The method is tested by simulating the behavior of a 3D aluminum–magnesium alloy tensile specimen subjected to uniaxial loading at constant nominal strain rate. The model predicts the influence of strain rate on the steady‐state flow stress of Al–Mg alloys, but no Portevin–Le Châtelier bands or serrated flow were observed in any of our simulations, and the influence of strain rate on tensile ductility is not predicted correctly. The reasons for this behavior and possible resolutions are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Microplasticity in HCF of Ti–6Al–4V

Previous research has shown that Ti–6Al–4V exhibits pronounced stress ratio effects under high cycle fatigue (HCF) loading. At high stress ratios (R>0.7), a transition of failure mode occurs from traditional surface fatigue crack initiation and growth to bulk-dominated damage initiation and coalescence of multiple microcracks consistent with a ductile tensile test. At these high stress ratios, ratchetting was shown to occur (Int. J. Fatigue 21 (1999) 679; Mech. Time-Dependent Mater. 2 (1999) 195), leading to progressive strain accumulation until final failure. This study explores the microstructural origins of this stress ratio transition in HCF using computational micromechanics. The material being studied is a two-phase Ti–6Al–4V plate forging, consisting of a duplex microstructure with a hexagonal close-packed (hcp) α-phase and lamellar grains with layers of body-centered cubic (bcc) β-phase and secondary hcp α-phase. Crystallographic slip is the dominant mode of plastic deformation in this material. A 2-D crystal plasticity model that incorporates nonlinear kinematic and isotropic hardening at the slip system level is implemented into the finite element method to simulate the cyclic plasticity behavior. The finite element model is used to qualitatively understand the distribution of microplasticity in this alloy under various loading conditions. For typical HCF stress amplitudes, it is shown that microstructure scale ratchetting becomes dominant at R=0.8, but is insignificant at R=0.1 and 0.5. Reversed cyclic microplasticity is insignificant at all three stress ratios. The effects of phase morphology and orientation distribution are shown to affect the microscale plastic strain distribution in terms of the location and magnitudes of the plastic shear bands that form within clusters or chains of primary α grains. The results of the finite element modeling are also considered in light of previous experimental results.     

The evolution of the stress–strain fields near a fatigue crack tip and plasticity-induced crack closure revisited

The evolution of the stress–strain fields near a stationary crack tip under cyclic loading at selected R‐ratios has been studied in a detailed elastic–plastic finite element analysis. The material behaviour was described by a full constitutive model of cyclic plasticity with both kinematic and isotropic hardening variables. Whilst the stress/strain range remains mostly constant during the cyclic loading and scales with the external load range, progressive accumulation of tensile strain occurs, particularly at high R‐ratios. These results may be of significance for the characterization of crack growth, particularly near the fatigue threshold. Elastic–plastic finite element simulations of advancing fatigue cracks were carried out under plane‐stress, plane‐strain and generalized plane‐strain conditions in a compact tension specimen. Physical contact of the crack flanks was observed in plane stress but not in the plane‐strain and generalized plane‐strain conditions. The lack of crack closure in plane strain was found to be independent of the material studied. Significant crack closure was observed under plane‐stress conditions, where a displacement method was used to obtain the actual stress intensity variation during a loading cycle in the presence of crack closure. The results reveal no direct correlation between the attenuation in the stress intensity factor range estimated by the conventional compliance method and that determined by the displacement method. This finding seems to cast some doubts on the validity of the current practice in crack‐closure measurement, and indeed on the role of plasticity‐induced crack closure in the reduction of the applied stress intensity factor range.     

An analysis of impact-induced deformation and fracture modes in amorphous glassy polymers

The finite deformation response of a planar block of polymer material subject to impact loading is analyzed using two constitutive models for glassy polymers, a reference Drucker–Prager type model and a physics-based macromolecular model, supplemented by a phenomenological model for craze initiation and widening. Full transient finite element analyses are carried out using a Lagrangian formulation of the field equations. The analyses allow an assessment of possible failure mechanisms under dynamic loading and the ability of the different models to predict such behavior. The results highlight the effect of the stress–strain behavior of polymers, notably the post-yield softening and large strain hardening, on localization of plastic flow. This behavior is adequately captured only by the macromolecular model.     

Elastic-Plastic Analysis Under Proportional and Non-Proportional Loading Paths Using Deformation Plasticity Theory

Abstract

An estimation of elastic-plastic stresses and strains is presented for mechanical components, using pseudo elastic analysis based on the deformation theory of plasticity. Analysis of two applications, one under proportional loading and other under non-proportional loading paths using pseudo elastic finite element method, is presented. A rectangular plate with a hole under tension loading and a rectangular plate fixed at one end under bending-tension non-proportional loading are considered for analysis. Pseudo Elastic finite element analysis for proportional loading uses elastic solutions and varies material properties for elements in plastic zone to estimate elastic-plastic solution. A finite element code is developed based on pseudo elastic analysis method. An attempt is made to extend pseudo elastic analysis to analyze bending-tension non-proportional loading problem. Both applications in consideration are assumed to be of Von Mises material and follow isotropic hardening rule with elastic-linear hardening material model. Non-linear analysis of the plate with a hole under proportional tensile loading and that of rectangular plate under bending-tension non-proportional loading are performed in ANSYS and results are compared for validation and are observed to be in good agreement with present analysis.