Micromechanical Constitutive Model Research Articles

A crystal plasticity-based micromechanical model for precipitate shearing: Application to cyclic softening of polycrystalline Ni-based superalloys

Cyclic deformation of polycrystalline Ni-based superalloys leads to cyclic hardening followed by softening, in terms of the mechanical response. A micromechanical constitutive model is proposed and implemented in a dislocation density-based, crystal plasticity framework to simulate the shearing of γ′ precipitates, which leads to the observed cyclic softening. The framework accounts for physically based deformation mechanisms. A slip-system level backstress model has been implemented to account for the kinematic hardening. Further, a micromechanical model for microstructure evolution due to precipitate shearing is developed that accounts for the dislocation-precipitate interactions and the resultant change in precipitate strengthening. The model is used to simulate cyclic deformation in two polycrystalline Ni-based superalloys, with different microstructures (in terms of the shape, size and volume fraction of precipitates), referred as Alloy 1 and Alloy 2. Room temperature cyclic deformation tests, followed by microstructure characterization were performed at different strain amplitudes for Alloy 1 to validate our predictions. For Alloy 2, the experimental stress–strain response was used from the literature to fit and validate our predictions. It is shown that the model can predict cyclic softening due to precipitate shearing for different initial microstructures and a range of loading conditions in polycrystalline Ni-based superalloys.

Influence of interphase type and thickness on the interface properties and tensile damage evolution of C/SiC composites

In this paper, the influence of interphase type (i.e. single-phase (PyC) and co-deposited (PyC+SiC)) and thickness (i.e. 300, 600, 1000, and 2000 nm) on the interface properties and damage evolution of mini-C/SiC composites under cyclic loading/unloading tension was investigated. The micromechanical constitutive model was adopted to derive the damage parameter of inverse tangent modulus (ITM) and perform the hysteresis analysis to estimate the interface properties of the mini-C/SiC composites with large debonding energy. Experimental damage evolution of the ITMs with unloading or reloading stress was analyzed for different interphase types and thickness. The interface properties (e.g. the interface debonding stress and interface debonding energy) were obtained through the hysteresis analysis. Relationships between the loading/unloading ITMs, interface properties, and interphase type and thickness were established.

Development of Micro-mechanical Constitutive Model for Alumina at High Strain Rates Using Unified Mechanics Theory

Ceramic materials used in mechanical applications show variations in their properties due to the presence of cracks. Micro-cracks within the material (size, orientation and density) affect the ceramic material’s strength and other mechanical properties. This study developed a micro-mechanics-based model that accounts for the original orientation of micro-cracks and their propagation as wing cracks. Unlike other micromechanics-based models, the current model defines failure based on entropy associated with crack propagation within the material. Entropy is calculated from energy dissipation from crack propagation from the pre-existing flaws in the ceramic. The Unified Mechanics Theory (UMT) is used to define entropy-based damage in the ceramic material, in which a parameter called thermodynamic state index (TSI) is employed to describe the state of the material. A representative volume element (RVE) with a pre-existing flaw is used to calculate the energy dissipated during the wing crack propagation. The effect of various crack lengths and orientations is incorporated with a probability density function. The strain rate effects are implemented using dynamic crack growth law. The stress-strain curve at strain rate from quasi-static to high strain rate (10-3-106) is plotted for Alumina under dynamic compression.

EFFECTS OF CYCLIC TRAFFIC LOADS AND SEAWATER EROSION ON SUFFUSION OF CRUSHED CALCAREOUS SANDS

Calcareous sands, in contrast to ordinary terrestrial source sands, are characterized by their propensity for fragmentation. This leads to the fracturing of calcareous sands within the foundation under the impact of traffic loads. The crushed calcareous sands then experience suffusion due to cyclic wave action, potentially causing foundation settlement. However, limited research has been conducted on the effects of varying load frequencies and magnitudes on road foundations subjected to cyclic traffic loads. In this study, a series of numerical case studies employing the coupled computational fluid dynamics and the discrete element method (CFD-DEM) are conducted. The macroscopic and microscopic effects of load magnitude and frequency on fines loss mass, fines loss rate, soil surface displacement, and microstructure are analyzed. The results indicate that as the traffic load magnitude increases and frequency decreases, fines loss mass and volumetric strain of the soil decrease, reducing the suffusion effect on the foundation. These findings provide valuable insights for the development of micromechanical constitutive models for calcareous sands and the design of transportation infrastructure.

Micromechanical modeling of the effects of crystal content on the visco-hyperelastic-viscoplastic behavior and fracture of semi-crystalline polymers

In this work, we present a novel physically based visco-hyperelastic-viscoplastic micromechanical constitutive model, which establishes a link between the evolution of the macromolecular network properties to the mechanical and fracture behavior of variable-crystallinity semi-crystalline polymers. Unlike previous micromechanical constitutive models that were only time independent, we propose a time-dependent scheme. It employs the computational effective eight-chain model for micro-macro transition while assuming a composite structure for the polymer. Thus, an innovative approach that couples the deformation and damage of individual polymer chains is developed. The proposed constitutive framework assumes that the stress developed through the deformation of semi-crystalline polymers is the sum of a macromolecular network and an intermolecular part. The macromolecular part accounts for the conformational change associated with Kuhn segments reorientation and the bond potential associated with the deformation of the bonds between Kuhn segments. Meanwhile, the intermolecular part accounts for the deformation of the crystalline and the amorphous phases. The constitutive equations are integrated using a mixed explicit/implicit integration algorithm. To validate and calibrate our model, we utilize uniaxial tensile experimental data obtained from three different polyethylene materials with varying crystallinity levels and different strain rates. We propose a robust calibration procedure, ensuring the identification of a single set of parameters that remain independent of crystal content and strain rate. Finally, we assess the model's predictive capabilities in predicting the mechanical behavior and fracture at different strain rates for variable-crystallinity polyethylene is evaluated. This comprehensive approach enhances our understanding and predictive capacity in modeling the intricate mechanical response up to fracture of semi-crystalline polymers under diverse conditions.

A micromechanical cyclic constitutive model for ratchetting deformation of polymeric composites with imperfect interface

AbstractIn this study, a micromechanical cyclic constitutive model for accurately describing the ratchetting deformation of polymeric composites is proposed. The model is based on the mean‐field homogenization method and incorporates the nonlinear viscoelastic‐viscoplastic (VE‐VP) cyclic constitutive model of the polymeric matrix and the imperfect interface. First, the nonlinear VE‐VP model was linearized using the incremental affine method and then was introduced into the homogenization process. The imperfect interface was represented using a linear spring model. A modified Mori‐Tanaka model was developed to incorporate the nonlinear VE‐VP model and imperfect interface into the micromechanical constitutive model. To implement the proposed micromechanical model, a numerical algorithm was developed. The model is capable of capturing the influence of the imperfect interface on the ratchetting deformation of polymeric composites. Furthermore, it is applicable to simulate various loading histories, including monotonic tension, stress relaxation, creep, and uniaxial ratchetting loads. The proposed model was validated by comparing its simulations with those obtained from the full‐field finite element method (FEM) model. The proposed model can predict the ratchetting deformation of polymeric composites and promote the practical application of these material in structures.Highlights A micromechanical cyclic constitutive model is developed to describe the ratchetting deformation of polymeric composites with imperfect interface. Nonlinear viscoelastic‐viscoplastic deformation of polymeric matrix is considered. A modified Mori‐Tanaka method is employed to incorporate the nonlinear constitutive model and imperfect interface into the process of homogenization. Good agreement between simulations of the proposed model and the full‐field FEM model under various loading histories.

A micromechanical constitutive model for porous ferromagnetic shape memory alloys under magneto-mechanical coupling

A micromechanical constitutive model for porous ferromagnetic shape memory alloys under magneto-mechanical coupling

A micromechanical constitutive model of high-temperature shape memory alloys

In this work, a new micromechanical constitutive model is constructed for high-temperature shape memory alloys. Different from the classical constitutive models, the microstructural patterns, heterogeneities of stress and strain fields at the microscopic scale are addressed. In the proposed model, three different inelastic deformation mechanisms, i.e., reversible martensitic transformation, irreversible transformation-induced plasticity, viscoplasticity, as well as their complex interactions, are considered. In addition to the well-known austenite and martensite phases, a new austenite-martensite interface phase is introduced to address the high local stress induced by the martensitic transformation. The modified Mori-Tanaka's homogenization scheme and Hill's interfacial operator are employed to determine the non-uniform stress fields of the three phases. To satisfy the thermodynamic compatibility of the proposed model, the driving forces and evolution equations of the three inelastic deformation mechanisms are derived based on the constructed Helmholtz free energy and the fundamental laws of irreversible thermodynamics. Inheritances of the plastic deformation induced by moving austenite-martensite (A-M) interface during repeated martensitic transformation and its reverse are incorporated. Temperature evolution caused by internal heat production and heat exchange with the ambient medium is also addressed. To validate the capability of the new constructed model, the predicted results of creep behavior and stress-assisted two-way shape memory effect of NiTiPd high-temperature shape memory alloys are compared with the experimental ones. The proposed model provides a theoretical tool for simultaneously analyzing the deformation behaviors at the macroscopic scale and underlying mechanisms at the microscopic scale.

Study of the Damage Evolution Process and Micromechanics Constitutive Model of Microcrystalline Limestone under Periodic Blasting Load

The cumulative damage to rock and soil mass caused by blasting in tunnel, highway, hydropower, and other projects is very complex, but the process of damage evolution is still unclear. This study took Zhujiapo mining area limestone as the research object and analyzed the change in its strength and mechanical parameters with periodic blasting loads. Combined with damage mechanics theory and microcrack propagation zone theory, a micromechanics constitutive model considering cumulative damage evolution was developed. The results show that (1) periodic blasting loads have a continuous cumulative effect on microcrystalline limestone, the peak strength and elastic modulus of which decrease exponentially with increasing blasting cycles; (2) periodic blasting loads cause crystal fractures, microcrack initiation, and propagation; and (3) the micromechanics damage constitutive model considering confining pressure and periodic blasting loads well describes the micromechanics behavior of microcrystalline limestone in the Zhujiapo mining area. The research results provide a theoretical reference to the study of rock damage mechanical properties under periodic blasting loads.

Effects of single-phase and co-deposited interphases on mechanical properties of T700TM-C/SiC minicomposites: experiment and theory prediction

ABSTRACT Experimental and theory investigations on the effects of single-phase (PyC) and co-deposited (PyC+SiC) interphases on the mechanical properties of T700TM-C/SiC minicomposites were conducted. Monotonic tensile tests and fiber’s push-in tests were conducted to obtain the minicomposite’s macro tensile mechanical properties and micro interface properties. The tensile strength was analyzed via a two-parameter Weibull distribution. The failure mechanism was obtained by fiber’s push-in tests and characterized by fracture morphology, and a damage-based micromechanical constitutive model was adopted to predict the tensile stress-strain response and interface debonding ratio (η) of C/SiC minicomposites with different interphases. For C/SiC, the experimental tensile curves were linearly till final tensile fracture with the lowest tensile strength and failure strain, due to the low interface shear strength (i.e., τ iss = 50.8 ± 15.3 MPa). For C/(PyC)300 nm/SiC, the minicomposite with the moderate ISS (i.e., τ iss = 62.2 ± 5.9 MPa) possessed the highest tensile strength and failure strain with the highest interface debonding ratio (i.e., η max = 0.95). For C/(PyC+SiC)/SiC, the tensile strength and strain were both lower than those of C/(PyC)/SiC due to the lower η.

Estimate constituent properties of 3D needle-punched C/SiC composites from hysteresis loops

To improve the mechanical properties of fiber-reinforced ceramic-matrix composites (CMCs), it is necessary to establish the relationship between the composite’s constituent properties and macro mechanical properties. In this paper, a hysteresis-based micromechanical method was adopted to obtain the constituent properties of four different types of 3D needle-punched C/SiC composites. Hysteresis-based damage parameters (i.e., inverse tangent modulus (ITM), hysteresis width, residual strain, hysteresis modulus, and damage factor) were derived from the hysteresis theory. Through analysis of the experimental monotonic tensile and cyclic hysteresis curves, the composite’s constituent properties (i.e., interface properties and thermal residual stress, etc.) and mechanical properties (i.e., first matrix cracking stress, interface debonding stress, and ultimate tensile strength, etc.) were obtained. Relationship between the composite’s constituent properties and mechanical properties was established. Using the estimated composite’s constituent properties and developed micromechanical constitutive models, the experimental monotonic and cyclic tensile loading/unloading curves were predicted.

Microstructure and tensile behavior of (BN/SiC)n coated SiC fibers and SiC/SiC minicomposites

Interphase plays an important role in the mechanical behavior of SiC/SiC ceramic-matrix composites (CMCs). In this paper, the microstructure and tensile behavior of multilayered (BN/SiC)n coated SiC fiber and SiC/SiC minicomposites were investigated. The surface roughness of the original SiC fiber and SiC fiber deposited with multilayered (BN/SiC), (BN/SiC)2, and (BN/SiC)4 (BN/SiC)8 interphase was analyzed through the scanning electronic microscope (SEM) and atomic force microscope (AFM) and X-ray diffraction (XRD) analysis. Monotonic tensile experiments were conducted for original SiC fiber, SiC fiber with different multilayered (BN/SiC)n interfaces, and SiC/SiC minicomposites. Considering multiple damage mechanisms, e.g., matrix cracking, interface debonding, and fibers failure, a damage-based micromechanical constitutive model was developed to predict the tensile stress-strain response curves. Multiple damage parameters (e.g., matrix cracking stress, saturation matrix crack stress, tensile strength and failure strain, and composite’s tangent modulus) were used to characterize the tensile damage behavior in SiC/SiC minicomposites. Effects of multilayered interphase on the interface shear stress, fiber characteristic strength, tensile damage and fracture behavior, and strength distribution in SiC/SiC minicomposites were analyzed. The deposited multilayered (BN/SiC)n interphase protected the SiC fiber and increased the interface shear stress, fiber characteristic strength, leading to the higher matrix cracking stress, saturation matrix cracking stress, tensile strength and fracture strain.

Superelasticity degradation of NiTi shape memory alloy in wide ranges of temperature and loading level: Experimental observation and micromechanical constitutive model

In this work, cyclic tension-unloading tests with different peak strains (10%-18%) in the temperature range from 313 K to 393 K are performed to investigate the effects of temperature and loading level on the cyclic deformation behavior of NiTi shape memory alloy (SMA) wires. Experimental results demonstrate that the superelasticity degradation occurs during the cyclic deformation process, and such phenomenon aggravates with the rise of ambient temperature and loading level, which can be attributed to the complex interactions among the martensite transformation (MT), austenite plasticity (AP), martensite plasticity (MP) and the transformation-induced plasticity (TRIP). Then, a micromechanical cyclic constitutive model is proposed based on the framework of irreversible thermodynamics and Eshelby's inclusion theory. The martensite (M) phase is treated as mobile inclusions with alterable eigenstrain embedded in the austenite (A) phase matrix. The volume fractions of the M-phase, A-phase, and A-M interface-phase are introduced. The non-uniform stress fields in the three phases are estimated by employing the Mori-Tanaka's homogenization scheme and interfacial operator. The driving forces of the four types of the inelastic deformation mechanisms, MT, AP, MP, and TRIP are derived based on the proposed new Helmholtz free energy, instantaneous growth hypothesis of M domains, and the energy dissipation inequality. The inheritances of the plastic deformation induced by the movement of A-M interfaces during the repeated MT and its reverse are incorporated. Finally, to validate the predictive capability of the proposed model, the predicted results for the superelasticity degradation of NiTi SMA with various peak strains at different ambient temperatures are compared with the experimental ones. Moreover, the dominant plastic deformation mechanisms and the effects of AP, MP, TRIP on the cyclic deformation of NiTi SMA are discussed.

On behaviors of porous shape memory polymer under different loading conditions

Shape memory polymer (SMP) has drawn much attention in the fields of aerospace, microsystems and biomedicine as a typical smart material with unique shape memory properties. The porous SMPs (P-SMPs) have been manufactured for the applications of reduce noise and insulate thermal. A constitutive model of P-SMPs that proposed based on phase transition theory has been investigated in this work. First, combining Mori–Tanaka method and phase transition theory, a modified micromechanics constitutive model of P-SMPs has been presented to describe the thermal-mechanical behavior of P-SMPs. Then, a series of experiments including uniaxial tension, stress relaxation and thermal cycling test have been conducted to determine the parameters of the modified constitutive model. Finally, the correctness of the proposed constitutive model has been verified by comparing the results of the thermodynamic cycle process including heating recovery and cooling loading stages obtained by the numerical simulation results and thermodynamic cycle experiment. The results show that with a porosity f = 0.1, the strain and stress mean square errors of the constitutive model based on the phase transition theory are 0.22 and 0.0102, respectively, which means that the constitutive model proposed based on phase transition theory can reflect the shape memory properties of P-SMP materials.

Implementation of Johnson-Holmquist-Beissel model in four-dimensional lattice spring model and its application in projectile penetration

• The 4D-LSM is further developed by implementing JHB constitutive model. • The JHB-4D-LSM was verified by modelling Brazilian tests and dynamic spalling tests. • JHB-4D-LSM is applied to study penetration in both thin plate targets and thick B 4 C under various impact velocities. • Good agreement among numerical simulation and numerical/ analytic results demonstrates the capability of JHB-4D-LSM. The imbedded linear constitutive model in four-dimensional lattice spring model (4D-LSM) is not sufficient or accurate enough to solve the dynamic problems with high-speed impacts. In order to produce a more realistic prediction of dynamic fracture process in brittle materials, the capability of four-dimensional lattice spring model (4D-LSM) has been further extended by implementing Johnson-Holmquist-Beissel (JHB) model. This is achieved by defining the micromechanical constitutive model parameters of 4D-LSM through the macro-scale strength parameters in JHB model, with an incremental form of 4D-LSM being developed. The incremental JHB-4D-LSM model is verified by modelling dynamic Brazilian tests and dynamic spalling tests, with good agreement between modelling results by JHB-4D-LSM and theoretical/numerical solutions in literature being obtained. For the demonstration of model application, the proposed JHB-4D-LSM model is applied to simulate and analyse the problems of projectile penetration with various initial impact speeds. Reasonable numerical modelling results indicate that, the proposed JHB-4D-LSM model can be served a promising tool to predict projectile penetration behaviour of brittle materials.

Thermal aging coupled with cyclic fatigue in cross-linked polymers: Constitutive modeling & FE implementation

A micro-mechanical constitutive model is presented to predict the concurrent effects of thermal aging and cyclic fatigue on the constitutive behavior of cross-linked polymers. The damage associated to each of those aging conditions is induced by mechanisms that have been extensively studied individually. Here, the main goal was to model the damage accumulated when those mechanisms work in parallel. In this respect, we modeled the effect of each aging condition separately through their corresponding aging mechanisms and then coupled them using the concept of network alteration platform. Accordingly, kinetic equations describing damage of each aging-mechanisms are coupled into the network alteration modular concept to allow consideration of mechanical and environmental damages synergies on the constitutive response of the polymer matrix. Following our recent models of thermal-oxidative aging, cyclic fatigue, and damage accumulation a model is developed based on the assumption of the full independence of mechanical and environmental damages. The model is implemented into finite element simulations. For validation, the devised model is bench-marked against a comprehensive set of experimental data. The proposed model shows promising results with reasonable precision.

A micromechanical constitutive model for porous ferromagnetic shape memory alloys considering magneto-thermo-mechanical coupling

In this work, a three-phase constitutive model describing the magneto-thermo-mechanical behaviors of porous Ferromagnetic Shape Memory Alloys (FSMAs) is established through a combination of micromechanical and thermodynamic theories. The kinetic equation is obtained in accordance with the thermodynamic driving force caused by the reduction of Gibb’s free energy of porous FSMAs. The thermodynamic driving force in combination with the corresponding resistance is used to establish the balance equation for calculating the volume fractions of martensitic variants under the action of different given magnetic fields, stresses and temperatures. Good agreement between the theoretical prediction of dense FSMA models and published experimental data is observed. The mechanical behaviors of porous FSMAs under magneto-thermo-mechanical coupling with different porosities and initial conditions are then discussed, which will provide a reliable theoretical basis for the future research of these functional materials as sensors or actuators.

Micromechanical constitutive modeling of tensile and cyclic behaviors of nano-clay reinforced metal matrix nanocomposites

Metal matrix nanocomposites are emerging rapidly among both research and industry communities. Nonetheless, the studies for their use in Low-Cycle Fatigue (LCF) applications are rarely documented. Prior to tailoring the microstructure for the desired LCF performance, it is a fundamental task to understand the structure-property correlations of the nanocomposites. In the present paper, a continuum-based micromechanical model starting from the nanostructure is proposed to fulfill such a task. The proposed model is applied to a piston aluminum alloy reinforced with 1 wt% nano-clay subjected to fully-reversed strain-controlled LCF loading at room temperature. The model, formulated within Eshelby's inclusion framework, considers the active clay/matrix interactions, the intercalation/exfoliation effect via the equivalent stiffness method, and the size effect through the introduction of the interphase thickness as a characteristic length scale. To render the model able to reproduce the cyclic hysteretic behavior of the nanocomposites, the isotropic/kinematic hardening rule is considered to describe the aluminum alloy plasticity. The model results are favorably compared to the experimental observations in terms of monotonic and cyclic elastoplastic stress-strain responses of the aluminum/clay nanocomposite. A parametric study is then carried out in order to understand the separate and synergic effects of clay weight fraction, clay geometrical parameters (e.g., shape and size), and clay structural parameters (e.g., number of silicate layers and interlayer spacing) on the overall monotonic and cyclic responses of the present nanocomposite. The reinforcing effect of each parameter is discussed concerning the micromechanical model.

Modelling of micro-damage and intrinsic self-healing in unidirectional CFRP composite structures

This work presents a micromechanical constitutive model of an intrinsically self-healing unidirectional CFRP composite material. The model is implemented into Abaqus/Standard user material subroutine UMAT and validated using experimental results of three-point bending tests available in the literature. Tested specimens consist of thermally mendable bis-maleimide tetrafuran (2MEP4F), and GA045 unidirectional carbon fibres. The matrix material is modelled using the elastic-plastic micro-damage-healing constitutive model. On the other hand, the reinforcing fibres are modelled as linear elastic. A three-dimensional micromechanical model, based on principles of the Rule Of Mixtures, is employed to model the homogenised composite. Finally, a parametric analysis is conducted to evaluate the effect of various parameters on the damage evolution and the healing performance, and afterwards, the results are discussed. The validation results have shown that the developed constitutive model is able to accurately simulate the micro-damage and healing processes in the intrinsically self-healing unidirectional composite structures.

Micromechanical elastoplastic limit analysis of in-plane bending of Functionally Graded Pipe elbows

Pipe elbows, also known as pipe bends, are important components of a piping system. These curved elements are very flexible when compared to their straight counterparts, and are often responsible for reducing the reaction forces and moments within the piping system. However, due to large deformations, the elbows are more likely to exceed their stress limits. The effect of in-plane bending on plastic limit loads of Functionally Graded (FG) pipe bends is presented using three-dimensional non-linear finite element analysis and a micromechanical constitutive model. The effective properties of the material are estimated by the Mori–Tanaka homogenization scheme and the TTO plasticity model. The analysis was carried out for different loading cases, geometries and volume fraction distribution. The results showed that an FG elbow has a very distinct behavior comparatively to a similar homogeneous elbow made out of metal, specially in terms of limit moments and stress distribution. Finally, an analytical model to estimate the limit moment of FG elbows is presented.