Micromechanics of plastic deformation and phase transformation in a three-phase TRIP-assisted advanced high strength steel: Experiments and modeling

The micromechanics of plastic deformation and phase transformation in a three-phase advanced high strength steel are analyzed both experimentally and by microstructure-based simulations. The steel examined is a three-phase (ferrite, martensite and retained austenite) quenched and partitioned sheet steel with a tensile strength of ~980 MPa. The macroscopic flow behavior and the volume fraction of martensite resulting from the austenite–martensite transformation during deformation were measured. In addition, micropillar compression specimens were extracted from the individual ferrite grains and the martensite particles, and using a flat-punch nanoindenter, stress–strain curves were obtained. Finite element simulations idealize the microstructure as a composite that contains ferrite, martensite and retained austenite. All three phases are discretely modeled using appropriate crystal plasticity based constitutive relations. Material parameters for ferrite and martensite are determined by fitting numerical predictions to the micropillar data. The constitutive relation for retained austenite takes into account contributions to the strain rate from the austenite–martensite transformation, as well as slip in both the untransformed austenite and product martensite. Parameters for the retained austenite are then determined by fitting the predicted flow stress and transformed austenite volume fraction in a 3D microstructure to experimental measurements. Simulations are used to probe the role of the retained austenite in controlling the strain hardening behavior as well as internal stress and strain distributions in the microstructure.     

A continuum micromechanical theory of overall plasticity for particulate composites including particle size effect

Classical continuum micromechanics cannot predict the particle size dependence of the overall plasticity for composite materials, a simple analytical micromechanical method is proposed in this paper to investigate this size dependence. The matrix material is idealized as a micropolar continuum, an average equivalent inclusion method is advanced and the Mori–Tanaka's method is extended to a micropolar medium to evaluate the effective elastic modulus tensor. The overall plasticity of composites is predicted by a new secant moduli method based on the second order moment of strain and torsion of the matrix in a framework of micropolar theory. The computed results show that the size dependence is more pronounced when the particle's size approaches to the matrix characteristic length, and for large particle sizes, the prediction coincides with that predicted by classical micromechanical models. The method is analytical in nature, and it can capture the particle size dependence on the overall plastic behavior for particulate composites, and the prediction agrees well with the experimental results presented in literature. The proposed model can be considered as a natural extension of the widely used secant moduli method from a heterogeneous Cauchy medium to a micropolar composite.     

A concurrent micromechanical model for predicting nonlinear viscoelastic responses of composites reinforced with solid spherical particles

A concurrent micromechanical model for predicting nonlinear viscoelastic responses of particle reinforced polymers is developed. Particles are in the form of solid spheres having micro-scale diameters. The composite microstructures are idealized by periodically distributed cubic particles in a matrix medium. Each particle is assumed to be fully surrounded by polymeric matrix such that contact between particles can be avoided. A representative volume element (RVE) is then defined by a single particle embedded in the cubic matrix. A spatial periodicity boundary condition is imposed to the RVE. One eighth unit-cell model with four particle and polymer subcells is generated due to the three-plane symmetry of the RVE. The solid spherical particle is modeled as a linear elastic material. The polymeric matrix follows nonlinear viscoelastic behaviors of thermorheologically simple materials. The homogenized micromechanical relation is developed in terms of the average strains and stresses in the subcells and traction continuity and displacement compatibility at the subcells’ interfaces are imposed. A stress–strain correction scheme is also formulated to satisfy the linearized micromechanical and the nonlinear constitutive relations. The micromechanical model provides three-dimensional (3D) effective properties of homogeneous composite responses, while recognizing microstructural geometries and in situ material properties of the heterogeneous medium. The micromechanical formulation is designed to be compatible with general displacement based finite element (FE) analyses. Experimental data and analytical micromechanical models available in the literature are used to verify the capability of the above micromechanical model for predicting the overall composite behaviors. The proposed micromodel is also examined in terms of computational efficiency and accuracy.     

Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys

Except for the recoverable strain induced by phase transformation, NiTi alloys are very ductile even in the martensite phase. The purpose of the present paper is to study the influence of permanent deformation, which results from plastic deformation of martensite, on the mechanical behaviour of pseudoelastic NiTi alloys. Based on phenomenological theory of martensitic transformation and crystal plasticity, a new three dimensional micromechanical model is proposed by coupling both the slip and twinning deformation mechanisms. The present model is implemented as User MATerial subroutine (UMAT) into ABAQUS/Standard to study the influences of plastic deformation on the stress and strain fields, and on the evolution of martensite transformation. Results show that with the increasing of plastic deformation the residual strain increases and the phase transformation stress–strain curves from the martensite to austenite become steeper and less obvious. Both characteristics, stabilisation of martensite and impedance of the reverse transformation, due to plastic deformation are captured.     

Three-dimensional micromechanical modeling of voided polymeric materials

A three-dimensional micromechanical unit cell model for particle-filled materials is presented. The cell model is based on a Voronoi tessellation of particles arranged on a body-centered cubic (BCC) array. The three-dimensionality of the present cell model enables the study of several deformation modes, including uniaxial, plane strain and simple shear deformations, as well as arbitrary principal stress states.The unit cell model is applied to studies on the micromechanical and macromechanical behavior of rubber-toughened polycarbonate. Different load cases are examined, including plane strain deformation, simple shear deformation and principal stress states. For a constant macroscopic strain rate, the different load cases show that the macroscopic flow strength of the blend decreases with an increase in void volume fraction, as expected. The main mechanism for plastic deformation is broad shear banding across inter-particle ligaments. The distributed nature of plastic straining acts to reduce the amount of macroscopic strain softening in the blend as the initial void volume fraction is increased. In the case of plane strain deformation, the plastic flow is observed to initiate across inter-particle ligaments in the direction of constraint. This particular mode of deformation could not have been captured using a two-dimensional, plane strain idealization of cylindrical voids in a matrix.The potential for localized crazing and/or cavitation in the matrix is addressed. It is observed that the introduction of voids acts to relieve hydrostatic stress in the matrix material, compared to the homopolymer. It is also seen that the predicted peak hydrostatic stress in the matrix is higher under plane strain deformation than under triaxial tension (with equal lateral stresses), for the same macroscopic stress triaxiality.The effect of void volume fraction on the macroscopic uniaxial tension behavior of the different blends is examined using a Considère construction for dilatant materials. The natural draw ratio was predicted to decrease with an increase in void volume fraction.     

Multiscale modeling of the damaged plastic behavior and failure of Al/SiCp composites

We studied the tensile behavior and damage of an aluminium X2080 reinforced with different volume fractions of silicon carbide particles. The main damage mechanism is particle failure. Regions of the matrix adjacent to broken particles are sites with high hydrostatic tension and hence the nucleation of cavities is expected. Using J integral and HRR modified solution it is possible to calculate the growth of these voids. Macroscopic failure is governed by a critical volume fraction of voids. The originality of this work lies in the modeling of the composite using a micromechanical approach.     

Particle fracture in high-volume-fraction ceramic-reinforced metals: Governing parameters and implications for composite failure

Weibull parameters of angular alumina particles are determined from experimental tensile test data on high-ceramic-content metal matrix composites using a micromechanical model that accounts for internal damage in the form of particle cracking, the dominant damage mode in these composites. The fraction of broken particles is assessed from the drop of Young's modulus and particle fracture is assumed to be stress controlled. Two extreme load-sharing modes, namely a purely local and a global load-sharing mode, are considered to account for the load redistribution due to particle fracture. Consistent powder strength parameters can be thus “back-calculated” for particles that are embedded in different Al-Cu matrices. On the other hand, this calculation fails for pure Al matrix composites, which exhibit a much larger strain to failure than Al-Cu matrix composites. It is shown that for Al matrix composites, the role of plastic (composite) strain on particle fracture constitutes a second parameter governing particle damage. This finding is rationalized by particle-particle interactions in these tightly packed ceramic particle-reinforced composites, and by the increase of matrix stress heterogeneity that is brought with increasing plastic strain. Failure of the alloyed matrix composites is well described by the (lower bound) local load-sharing micromechanical model, which predicts a catastrophic failure due to an avalanche of damage. The same model predicts failure of pure aluminium matrix composites to occur at the onset of tensile instability, also in agreement with experimental results once the role of plastic strain on damage accumulation is accounted for.     

On hindered settling of particles of different sizes

The flow of a non-dilute fluid suspension is considered in which the dispersed phase consists of particles or droplets of different sizes. A phenomenological two-phase flow theory is formulated for both continuous and discrete distributions of particle sizes and illustrated by considering the batch settling of such a mixture. The volume fractions and particle distribution functions are determined, as well as the composition of the sedimentary layer.     

Effect of phase-transformation on mechanical behavior of dual-phase steel plate

The mechanical behavior of dual phase steel plates is affected by internal stresses created during martensite transformation. Analytical modelling of this effect is made by considering a unit cell made of martensite inclusion in a ferrite matrix. A large strain finite element analysis is then performed to obtain the plane stress deformation state. Displayed numerically are the development of the plastic zone and distribution of local state of stress and strain. Studied also are the shape configuration of the martensite (hard-phase) that influences the interfacial condition as related to stress transmission and damage. Internal stresses are found to enhance the global flow stress after yield initiation in the ferrite matrix. Good agreement is obtained between the analytical results and experimental observations.     

SiC粒子非均布引起铝基复合材料的损伤分析

 根据电镜断面考察结果，以Gurson模型为本构方程的有限单元 法对包体模型及三维非均匀模型进行了详细分析. 为了评价应力-应变 关系及损伤的主要因素，考虑了基体中SiC粒子的体积率和径比的非均 匀分布. 其结果表明，用这种非均匀模型能很好地仿真铝基体在大量塑 性变形之后所发生的韧窝破坏过程. SiC粒子体积率、径比及其位置的 非均匀性，对局部和整体损伤过程与应力-应变关系的影响相当大. 当 Sic粒子径比为1.0，并在基体中均匀分布时，断裂应变会大幅度增大.     

The crack tip zone shielding effect for ductile particle reinforced brittle materials

The crack tip zone shielding effect for the ductile particle reinforced brittle materials is analyzed by using a micromechanics constitutive theory. The theory is developed here to determine the elastoplastic constitutive behavior of the composite. The elastoplastic particles, with isotropic or kinematical hardening, are uniformly dispersed in the brittle elastic matrix. The method proposed is based on the Mori-Tanaka's concept of average stress in the composite. The macroscopic yielding condition and the incremental stress strain relation of the composite during plastic deformation are explicity given in terms of the macroscopioc applied stress and the microstructural parameters of the composite such as the volume fraction and yield stress of ductile particles, elastic constants of the two phases, etc. Finally, the contribution of the plastic deformation in the particles near a crack tip to the toughening of the composite is evaluated. The project supported by National Natural Science Foundation of China     

A new formulation of the effective elastic–plastic response of two-phase particulate composite materials

In this paper the double-inclusion model, originally developed to determine effective linear elastic properties of composite materials, is reformulated and extended to predict the effective nonlinear elastic–plastic response of two-phase particulate composites reinforced with spherical particles. The resulting problem of elastic–plastic deformation of a double-inclusion embedded in an infinite reference medium subjected to an incrementally applied far-field strain is solved by the finite element method. The proposed double-inclusion model is evaluated by comparison of the model predictions to the available exact results obtained by the direct approach using representative volume elements containing many particles. It is found that the double-inclusion formulation is capable of providing accurate prediction of the effective elastic–plastic response of two-phase particulate composites at moderate particle volume fractions.     

A physically-based constitutive model for anisotropic damage in rubber-toughened glassy polymers during finite deformation

The present work focuses on the development of a physically-based model for large deformation stress-strain response and anisotropic damage in rubber-toughened glassy polymers. The main features leading to a microstructural evolution (regarding cavitation, void aspect ratio, matrix plastic anisotropy and rubbery phase deformation) in rubber-toughened glassy polymers are introduced in the proposed constitutive model. The constitutive response of the glassy polymer matrix is modelled using the hyperelastic-viscoplastic model of [Boyce et al., 1988] and [Boyce et al., 2000]. The deformation mechanisms of the matrix material are accounted for by two resistances: an elastic-viscoplastic isotropic intermolecular resistance acting in parallel with a visco-hyperelastic anisotropic network resistance, each resistance being modified to account for damage effects by void growth with a variation of the void aspect ratio. The effective contribution of the hyperelastic particles to the overall composite behaviour is taken into account by treating the overall system in a composite scheme framework. The capabilities of the proposed constitutive model are checked by comparing experimental data with numerical simulations. The deformation behaviour of rubber-toughened poly(methyl methacrylate) was investigated experimentally in tension at a temperature of 80 °C and for different constant true strain rates monitored by a video-controlled technique. The reinforcing phase is of the soft core-hard shell type and its diameter is of the order of one hundred nanometers. The particle volume fraction was adjusted from 15% to 45% by increments of 5%. The stress-strain response and the inelastic volumetric strain are found to depend markedly on particle volume fraction. For a wide range of rubber volume fractions, the model simulations are in good agreement with the experimental results. Finally, a parametric analysis demonstrates the importance of accounting for void shape, matrix plastic anisotropy and rubber content.     

Influences of initial porosity,stress triaxiality and Lode parameter on plastic deformation and ductile fracture

Local mechanical properties in aluminum cast components are inhomogeneous as a consequence of spatial distribution of microstructure,e.g.,porosity,inclusions,grain size and arm spacing of secondary dendrites.In this work,the effect of porosity is investigated.Cast components contain voids with different sizes,forms,orientations and distributions.This is approximated by a porosity distribution in the following.The aim of this paper is to investigate the influence of initial porosity,stress triaxiality and Lode parameter on plastic deformation and ductile fracture.A micromechanical model with a spherical void located at the center of the matrix material,called the representative volume element(RVE),is developed.Fully periodic boundary conditions are applied to the RVE and the values of stress triaxiality and Lode parameter are kept constant during the entire course of loading.For this purpose,a multi-point constraint(MPC)user subroutine is developed to prescribe the loading.The results of the RVE model are used to establish the constitutive equations and to further investigate the influences of initial porosity,stress triaxiality and Lode parameter on elastic constant,plastic deformation and ductile fracture of an aluminum die casting alloy.     

A combined viscoelastic–viscoplastic behavior of particle reinforced composites

This study formulates a micromechanical model for predicting effective viscoelastic–viscoplastic responses of composites. The studied composites consist of solid spherical particle reinforcements dispersed in a homogeneous matrix. The particle constituent is assumed linear elastic, while the matrix exhibits combined viscoelastic–viscoplastic responses. The Schapery integral model is used for the 3D isotropic non-linear viscoelastic responses. Two viscoplastic models are considered: the Perzyna model, having a rate-independent yield surface and an overstress function, and the Valanis endochronic model based on an irreversible thermodynamics without a yield surface. The Valanis model is suitable for materials when viscoplastic responses occur at early loadings (small stress levels). A unit-cell model with four particle and polymer sub-cells is generated to obtain homogenized responses of the particle-reinforced composites. Available micromechanical models and experimental data in the literature are used to verify the proposed micromechanical model in predicting effective time-dependent and inelastic responses of composites. Field variables in the homogenized composites are compared to the ones in heterogeneous composites. The heterogeneous composites, having detailed particle geometries, are modeled using finite element (FE) method.     

Crystal plasticity finite element modeling of mechanically induced martensitic transformation (MIMT) in metastable austenite

A new crystal plasticity model incorporating the mechanically induced martensitic transformation in metastable austenitic steel has been formulated and implemented into the finite element analysis. The kinetics of martensite transformation is modeled by taking into consideration of a nucleation-controlled phenomenon, where each potential martensitic variant based on Kurdjumov–Sachs (KS) relationship has different nucleation probability as a function of the interaction energy between externally applied stress and lattice deformation. Therefore, the transformed volume fractions are determined following selective variants given by the crystallographic orientation of austenitic matrix and applied stress in the frame of the crystal plasticity finite element. The developed finite element program is capable of considering the effect of volume change by the Bain deformation and the lattice-invariant shear during the martensitic transformation by effectively modifying the evolution of plastic deformation gradient of the conventional rate-dependent crystal plasticity finite element. The validation of the proposed model has been carried out by comparing with the experimentally measured data under simple loading conditions. Good agreements with the measurements for the stress–strain responses, transformed martensitic volume fractions and the influence of strain rate on the deformation behavior will enable the model to be promising for the future applications to the real forming process of the TRIP aided steel.     

Strain gradient plasticity analysis of transformation induced plasticity in multiphase steels

“To what extent do plastic strain gradients affect the strengthening resulting from the transformation of small metastable inclusions into hard inclusions within a plastically deforming matrix?” is the central question addressed here. Though general in the approach, the focus is on the behavior of TRIP-assisted multiphase steels. A two-dimensional embedded cell model of a simplified microstructure composed of a single metastable austenitic inclusion surrounded by a soft ferritic matrix is considered. The cell is inserted in a large homogenized medium. The transformation of a fraction of the austenite into a hard martensite plate is simulated, accounting for a transformation strain, and leading to complex elastic and plastic accommodation. The size of a transforming plate in real multiphase steels is typically between 0.1 and 2 μm, a range of size in which plastic strain gradient effects are expected to play a major role. The single parameter version of the Fleck–Hutchinson strain gradient plasticity theory is used to describe the plasticity in the austenite, ferrite and martensite phases. The higher order boundary conditions imposed on the plastic flow have a large impact on the predicted strengthening. Using realistic values of the intrinsic length parameter setting the scale at which the gradients effects have an influence leads to a noticeable increase of the strengthening on top of the increase due to the transformation of a volume fraction of the retained austenite. The geometrical parameters such as the volume fraction of retained austenite and of the transforming zone also bring significant strengthening. Strain gradient effects also significantly affect the stress state inside the martensite plate during and after transformation with a potential impact on the damage resistance of these steels.     

Dynamic-mechanical properties of interfacially modified glass sphere filled polyethylene

Model composites of spherical glass particles dispersed in a matrix of high density polyethylene were prepared both with and without interfacial modification by an azidofunctional trialkoxysilane. Dynamic mechanical measurements of the composites in the melt state were recorded. The unmodified composites behave as theoretically predicted and the effect of particle—particle interaction at high volume fractions can be measured. The composites with a modified interfacial region have greater shear moduli due to the effect of a region surrounding the particle modified by the silane. The material in this region is largely bound to the glass surface and was examined by Fourier transform infrared spectroscopy after extraction of the bulk matrix. Theoretical calculations are shown to be useful in calculating the mechanical properties and volume fraction of the interfacial region.     

The influence of particle shape,volume fraction and distribution on post-necking deformation and fracture in uniaxial tension of AA5754 sheet materials

Finite element analysis was performed over a small particle field, edge constraint plane strain post-necking model. The aim is to understand the roles of particle shape, volume fraction and distribution over the post-necking deformation and fracture of AA5754-O sheet materials. For models containing one single particle, the post-necking deformation decreases when the particle varies from circular to elliptical. The inter-particle spacing, the major parameter of distribution to determine whether a pair of particles belongs to a stringer or not, was varied for models with two particles of circular or elliptical shape. The general trend is that the post-necking deformation and fracture strains decrease with decreasing spacing between particles. There is considerable difference in terms of both fracture topographies and strains for models containing 16 particles when distributions varied from random/uniform to stringer distributions. The post-necking deformation and fracture strains monotonically decrease with particle volume fractions for models with 4–64 particles of random or stringer distribution. This indicates that the post-necking behavior for AA5754-O alloys where the matrix material is rather ductile is not solely controlled by a single or pair of particles although they may become initiation places of damage. Multiple damaging sources such as stringers or large particles can act cooperatively and speed up the damaging propagation of the material, and therefore produce small post-necking deformation and early fracture. The center clustering of particles can be beneficial for post-necking behavior and bendability of sheet materials.     

A Tensile Split Hopkinson Bar for Testing Particulate Polymer Composites Under Elevated Rates of Loading

A tensile split Hopkinson bar apparatus is developed for testing high strain rate behavior of glass-filled epoxy. The apparatus uses a specimen gripping configuration which does not require fastening and/or gluing and can be readily used for castable materials. Details of the experimental setup, design of grips and specimen, specimen preparation method, benchmark experiments, and tensile responses are reported. Also, the effects of filler volume fraction (0–30%) and particle size (11–42 μm) are examined under high rates of loading and the results are compared with the ones obtained from quasi-static loading conditions. The results indicate that the increase in the loading rate contributes to a stiffer and brittle material response. In the dynamic case lower ultimate stresses are seen with higher volume fractions of filler whereas in the corresponding quasi-static cases an opposite trend exists. However, the absorbed specific energy values show a decreasing trend in both situations. The results are also evaluated relative to the existing micromechanical models. The tensile response for different filler sizes at a constant volume fraction (10%) is also reported. Larger size filler particles cause a reduction in specimen failure stress and specific energy absorbed under elevated rates of loading. In the quasi-static case, however, the ultimate stress is minimally affected by the filler size.