Combined Constitutive Model Research Articles

Modeling and simulation of the negative angle cutting with a combined constitutive model for U71Mn rail steel

Due to the increasing train axle load, running speed and traffic volume, rails are prone to severe rolling contact fatigue (RCF) defects. Repairing the rail profile by milling is the latest technology to solve the above hidden problems, but there are few related studies in recent years. In this paper, the milling maintenance process of rails is studied by using finite element method(FEM). This study examines the fracture behavior of U71Mn steel rail under various stress triaxiality conditions, temperatures, and strain rates. An electronic universal testing machine is utilized to conduct the experiments, and a Johnson-Cook (J-C) failure model for U71Mn steel rail is developed. A 3D cutting simulation model was developed using the Johnson-Cook (J-C) combined constitutive model. The accuracy and reliability of the numerical simulation model were confirmed by comparing the cutting force and chip morphology obtained from both simulation and experimental results. The cutting simulation model had an error rate of within 10 % when predicting the cutting force. Following that, the fracture zone and chip portion of the tensile specimen were metallographically analyzed. The applicability of the ductile failure criterion in describing the observed failure in the U71Mn rail has been proven.

Elastoplastic augmented virtual internal bond modeling for rock: A fracture‐plasticity combined constitutive model

AbstractIn the ultra‐deep reservoir or other deep‐buried subsurface engineering, the in situ stress is high enough to make the rock transition from the brittle to the plastic. In such situation, the fracturing process always goes with the plastic deformation together. Therefore, to develop an elastoplastic constitutive model which can simultaneously account for both fracture and plastic deformation is critically important. In this paper, an elastoplastic augmented virtual internal bond (EP‐AVIB) model is developed. In EP‐AVIB, a hyperelastic AVIB is developed to characterize the elastic deformation of rock, in which the micro bond is linear elastic in compression whereas is hyperelastic in tension. The Drucker‐Prager yield criterion is employed to characterize the plastic deformation. Thus, the EP‐AVIB can combine the fracture and plastic deformation together. The simulation examples show that the EP‐AVIB can simulate the elastoplastic mechanical behaviors and the fracturing process of rock subjected to compression. It provides a simple approach to the elastoplastic failure simulation of rock. Its perspective in deep reservoir and deep‐buried subsurface engineering simulation should be inspiring.

A FDEM approach to study mechanical and fracturing responses of geo-materials with high inclusion contents using a novel reconstruction strategy

In this paper, a detailed FDEM approach to simulate the mechanical and fracturing responses of heterogeneous geomaterials with irregular inclusions is systematically developed. The inclusion surface morphology is first obtained through 3D scanning techniques. A computational geometry method, the curvature-weighted sphere Voronoi method (CWSVM), is adopted to control the mesh quantity and quality and ensure the efficiency and accuracy of the FDEM numerical model. A signed-distance-field-based discrete element method (SDF-DEM) is employed to approximate the natural distribution and orientation of inclusions. Heterogeneous geomaterials with large inclusion contents (such as 60% and 70%) are generated effectively and efficiently through this approach. Next, to model the fracturing process, a finite discrete element method (FDEM) model is developed by integrating cohesive elements into the mesh in a fast and efficient manner. In addition, a combined constitutive model is proposed to consider the shear-hardening behaviour of the cohesive elements. The proposed numerical approach is verified through comparison with experimental results, including the shape of inclusions and mechanical responses of geomaterials. The results demonstrate that both satisfactory precision and low calculation costs can be achieved using the proposed algorithm. The consequent simulation performance is verified through comparisons of observations and numerical results with experimental results for failure patterns and mechanical behaviours. In addition, the effects of the strength of the interfaces between the inclusions and matrix on the mechanical and fracturing characteristics of inclusion-containing geomaterials are analysed quantitatively. The mechanical strength decreases rather than increases with increasing content of inclusions when the interface strength is less than the matrix strength.

Deformation behavior and forming process simulation of semi-solid powder rolling based on the combined constitutive model

Semi-solid powder forming (SPF) as a novel technology has been widely used to prepare composite materials. However, most of the present models used to simulate the complicated SPF process are based on the constitutive relationship of single dense or porous material, which cannot well satisfy the actual conditions. In this study, the process of semi-solid powder rolling was simulated by the combined constitutive formula of sintered and dense Al-Cu-Mg alloy materials obtained from semi-solid compression experiments. The results show that the semi-solid compression curves of dense and sintered materials are similar, and their peak stresses increase with the decreasing porosities. The grain or particle size of sintered materials after semi-solid compression becomes finer as powders crushed, but the grain size of dense materials becomes larger due to grain coarsening and deformation, which is the key advantage of SPF with fine microstructures. The combined constitutive model of semi-solid powder materials was established and verified, and then the numerical simulation of semi-solid powder rolling based on the model was proved that can well describe the rolling process, which provides a guidance for process optimization.

Numerical modeling and constitutive model verification for high-strength automotive steel

In this paper, the quasi-static and dynamic tensile tests with a gauge length of 20 mm for dual-phase (DP) 780 steel were conducted under strain rates ranging from 10−3 to 103/s. The neglected details and differences between the quasi-static and dynamic tensile test conditions were investigated to develop an accurate numerical modeling method. A high-precision combination method for the empirical constitutive model was proposed and utilized in the developed numerical model to verify the ability of the constitutive model to reproduce the experimental data at different strain rates. The excellent results indicate that the adjusted determination coefficient of the constitutive model, the adjustable range of the extrapolation curves, and the proportion factor P in the combined constitutive model are the key parameters for accurately describing the quasi-static and dynamic mechanical behavior before and after the necking.

Double-edged cutting simulation with a new combined constitutive model for AISI 1045 steel

Due to chip-flow interference and coordination, the two types of chips formed in the processes of double-edged cutting make a remarkable difference to cutting force components, tool service life, and machined parts quality. However, the chip formation mechanisms of both types are poorly understood, and the existing constitutive models generally fail to capture the deformation characteristics of the workpiece material during double-edged cutting. To this end, a new combined constitutive model composed of plasticity and damage parts is presented and applied to the finite element (FE) model for double-edged cutting of AISI 1045. The plasticity part considers the impacts of strain, strain rate, and temperature on the flow stress of workpiece material. The damage part considers the effects of stress states on the equivalent plastic strain at damage initiation. Double-edged cutting simulations were carried out employing the combined constitutive model and the Johnson-Cook (JC) model, respectively. To validate the presented constitutive model, experiments for double-edged cutting of AISI 1045 were completed, and the predicted results were compared with experimental results. It is concluded that the presented constitutive model substantially enhances the predicting accuracy for chip morphologies and cutting force components compared to the JC model. In addition, the two types chip formation mechanisms in double-edged cutting are revealed through analyzing the chip generation in simulations and the chips collected from the experiments. The new combined constitutive model contributes to the simulation-based optimization of the tool/process parameters in double-edged cutting to reduce the cutting forces or produce the desired chip morphology.

Size effect on the shear damage under low stress triaxiality in micro-scaled plastic deformation of metallic materials

Micro-forming is one of the major micro-manufacturing methods with promising application potentials, in which the damage response and fracture behavior need to be insightfully addressed. Among all the damage criteria to predict fracture, GTN model is a widely-used one and able to predict void-dominated fracture in micro-scale deformation. However, it is not very applicable under low stress triaxiality and shear-dominated condition. An in-depth understanding of shear damage and its potential size effect are crucial to explore the micro-scaled damage and fracture mechanisms. This research characterizes the size effect on flow stress via employing a combined constitutive model, and an approach for applying a phenomenological shear damage evolution law to the GTN-Thomason model via considering the size effect is developed. The prediction of micro-scaled fracture in a wide stress triaxiality range is thus enabled. Through simulation and experiment, the proposed model is validated and verified. In addition, stress state parameters including stress triaxiality, Lode parameter, and weight function, are also discussed, and the two damage parameters are analyzed quantificationally to reveal different fracture mechanisms occurring in different stress states and grain sizes. The research thus facilitates the physical insight and in-depth understanding of the size effect on damage evolution and fracture formation in micro-scaled plastic deformation of materials.

Viscoelastic-viscoplastic combined constitutive model for glassy amorphous polymers under loading/unloading/no-load states

PurposeThis study aims to propose a novel viscoelastic–viscoplastic combined constitutive model for glassy amorphous polymers within the framework of thermodynamics at finite strain that is capable of capturing their rate-dependent inelastic mechanical behavior in wide ranges of deformation rate and amount.Design/methodology/approachThe rheology model whose viscoelastic and viscoplastic elements are connected in series is set in accordance with the multi-mechanism theory. Then, the constitutive functions are formulated on the basis of the multiplicative decomposition of the deformation gradient implicated by the rheology model within the framework of thermodynamics. Dynamic mechanical analysis (DMA) and loading/unloading/no-load tests for polycarbonate (PC) are conducted to identify the material parameters and demonstrate the capability of the proposed model.FindingsThe performance was validated in comparison with the series of the test results with different rates and amounts of deformation before unloading together. It has been confirmed that the proposed model can accommodate various material behaviors empirically observed, such as rate-dependent elasticity, elastic hysteresis, strain softening, orientation hardening and strain recovery.Originality/valueThis paper presents a novel rheological constitutive model in which the viscoelastic element connected in series with the viscoplastic one exclusively represents the elastic behavior, and each material response is formulated according to the multiplicatively decomposed deformation gradients. In particular, the yield strength followed by the isotropic hardening reflects the relaxation characteristics in the viscoelastic constitutive functions so that the glass transition temperature could be variant within the wide range of deformation rate. Consequently, the model enables us to properly represent the loading process up to large deformation regime followed by unloading and no-load processes.

Ratcheting and fatigue behavior of Eurofer97 at high temperature, part 2: modeling

A constitutive model is proposed for Reduced-Activation Ferritic-Martensitic (RAFM) steel Eurofer97 at high temperatures by combining formulae from previous modeling approaches to describe and predict mechanical behaviors under various cyclic loading conditions. Two failure modes, fatigue fracture and over-accumulated strain (ratcheting) are able to be simulated by the combined constitutive model. Cyclic softening and the effect of magnitude, symmetry and rate of external loading on ratcheting behavior are also able to be described by the new model. Parameter values are fitted based on strain-controlled and stress-controlled isothermal uniaxial experiments on Eurofer97 batch two at 450°C and 550°C. The simulated results are presented to compare with corresponding experimental data, to show the performance of the new constitutive model.

Simplified simulation of the installation of vibro-piles in water saturated soil

This paper presents a novel and simplified approach to simulate the effects of the vibro-pile installation on the deformation of deep excavation shoring walls at high ground water levels. Although commonly-used finite element simulations provide acceptable predictions of the wall displacements caused by underwater excavations, anchor installation, or pit dewatering processes, they could not explain the unexpected large wall movements measured in different excavations during the vibro-pile installation stage. Previous dynamic finite element simulations of the vibro-installation of a single pile showed that after few cycles the effective stress in the soil surrounding the pile reduces almost near to zero. The soil region affected was called “the liquefaction zone”. Due to the waves emanating from the pile, the soil beyond the liquefaction zone is subjected to a (high-) cyclic loading, i.e. a large number of strain cycles with small amplitude. When the soil behavior is modeled with hypoplasticity or elastoplasticity, its response to these small strain amplitudes is nearly (hypo)elastic resulting in an erroneous accumulation of stress or strains, see Osinov (2017) [1]. Based on this observation, Osinov et al. (2015) [2,3] suggested that the accumulation effects caused by many cycles of small strain amplitude could explain the large wall displacements observed during the pile installation. Following this idea, in this paper we model the soil behavior with a combination of hypoplasticity (which can be applied to cycles of large strain amplitudes and monotonic paths) and the high cyclic accumulation (HCA) model, which is able to extrapolate the accumulation of stress/strain caused by a large number of cycles of small strain amplitude (ϵampl<10−3). The pile installation is not explicitly modeled, but its effects are incorporated in the numeric model by applying a field of cyclic strain amplitudes around each pile. Using this combined constitutive model and simulation technique, the behavior of the shoring of an excavation pit in Potsdamer Platz, in Berlin was simulated under quasi-static conditions in a finite element program. The obtained simulation results are in good agreement with the horizontal displacement of the diaphragm wall measured during the entire construction stages, including the underwater excavation and the pile installation.

Stress–Strain Modeling and Brittleness Variations of Low-Clay Shales with CO2/CO2-Water Imbibition

A better understanding of the stress–strain behaviors of shale samples after shale-CO2 or shale-water–CO2 interactions is of great importance to CO2 enhanced shale gas exploitation and CO2 sequestrating in shale reservoirs. In this study, a constitutive model that combines with the modified Duncan–Chang model and Weibull distribution-based model is applied to investigate the stress–strain characteristics of low-clay shale samples treated by sub-/super-critical CO2 and sub-/super-critical CO2 + water for different times (10 days, 20 days, and 30 days). The results show that the model could describe well the crack closure stage, the elastic stage, and the inelastic stage of shale samples. The axial strain at the connection point between the two models varies from 28.51 to 43.36% of the axial strain at the failure point. Shale-CO2 or shale-water–CO2 interactions make shale samples more ductile at the crack closure stage, which can be depicted as the increase of initial elastic modulus during the imbibition process. The brittleness index values (BI) which are calculated based on the combined constitutive model increase with increasing soaking time for shale samples treated by sub-/super-critical CO2, and decrease with increasing soaking time for shale samples treated by sub-/super-critical CO2 + water.

Influence of size effect and plastic strain gradient on the springback behaviour of metallic materials in microbending process

In micro-bending process, the size effect induced by the variation of grain size and geometrical size (the thickness) of sheet metals, represented by the ratio of surface grain number to the total grain number of workpiece (η), and strain gradient effect are the key factors affecting the bending behaviour and springback angle. The interaction of the grain-based size effect and the strain gradient effect on springback has not yet been fully understood and investigated in micro-scaled bending of metallic materials. In this research, a combined constitutive model simultaneously considering both the grain size effect and strain gradient was proposed. The theoretical calculation was conducted using the proposed model, and quantitative evaluation was made of the contribution from each kind of size effect on the springback angle. The springback angle due to strain gradient size effect decreases with the increase of sheet thickness and the decrease of the grain size. Pure microbending experiments using copper alloy sheet metal samples with the thickness of 0.1, 0.2, and 0.4 mm were conducted, and the springback angles calculated using the established model were corroborated by the experimental results, providing model validation. The reported results thus provide an in-depth understanding of the grain-geometrical size effect and strain gradient size effect influence on the springback behaviour in micro-bending of metallic materials.

A new constitutive equation for solid propellant with the effects of aging and viscoelastic Poisson’s ratio

A new constitutive equation for solid propellant with the effects of aging and viscoelastic Poisson’s ratio is proposed. Effects of thermo-oxidative aging and viscoelastic Poisson’s ratio are considered in this comprehensive constitutive equation with two sets of reduced time system coping with the time and temperature dependence. In order to simulate the single and combined effects of aging and viscoelastic Poisson’s ratio, constitutive equation is rewritten into an incremental form and implemented in the user subroutine UMAT at the platform of finite element code ABAQUS. Detailed procedure for acquiring the parameters in constitutive equation is introduced and conducted for the subsequent applied analysis. Two typical loading cases during the service life of solid rocket motor and four sets of combined constitutive models are simulated. Von Mises strain and stress distribution and their changes versus time are utilized as the main analysis index. The results show that the effects of aging and viscoelastic Poisson’s ratio or their combinations will improve or decrease the level and change the distribution of Von Mises strain and stress in varying degrees.

Combined constitutive model for creep and steady flow rate of frozen soil in an unconfined condition

A combined constitutive model is developed for the creep behavior of frozen soil in an unconfined condition. The model is obtained by coupling two stress- and time-dependent models, which are responsible for the primary and tertiary creep stages. The model parameters are dependent on temperature and can be readily determined from the strain rate–time curves at two creep stresses. The model performance is demonstrated by simulating the complete strain–time and strain rate–time curves (including primary, secondary, and tertiary stages) of frozen sand and frozen clay in uniaxial creep tests under different creep stresses. Moreover, two equations are obtained from the combined model. One shows a good capability in describing the relationship between creep strength and the time to creep failure. The other makes an excellent prediction of the steady flow rate in a typical creep process. Both equations can reflect the effects of stress and temperature on the creep behavior of frozen soil.

Applicability of micro–macro decoupling scheme to two-scale analysis of fiber-reinforced plastics

The numerical study is made to demonstrate the applicability of the method of decoupling multi-scale analysis to the micro–macro evaluation of the mechanical behavior of fiber-reinforced plastics (FRP) that exhibits inelastic deformations and internal damage of the matrix material. During the course of this demonstration, it is confirmed that the reliability of the decoupling method can be guaranteed if the macroscopic constitutive model is introduced so as to inherit the microscopic material behavior. To this end, with reference to the results of the numerical material testing on the periodic microstructures of FRP, we propose an anisotropic elastoplastic-creep-damage combined constitutive model to represent the macroscopic material behavior and illustrate the characteristics of the inelastic deformations that resemble the material behavior assumed for plastics at micro-scale. With the identified macroscopic material parameters, the macroscopic structural analysis, which is followed by the localization analysis consistently, can be an actual proof of the utility value of the decoupling method in practice.

A theoretical and non-destructive experimental approach for direct inclusion of measured collagen orientation and recruitment into mechanical models of the artery wall

Gradual collagen recruitment has been hypothesized as the underlying mechanism for the mechanical stiffening with increasing stress in arteries. In this work, we investigated this hypothesis in eight rabbit carotid arteries by directly measuring the distribution of collagen recruitment stretch under increasing circumferential loading using a custom uniaxial (UA) extension device combined with a multi-photon microscope (MPM). This approach allowed simultaneous mechanical testing and imaging of collagen fibers without traditional destructive fixation methods. Fiber recruitment was quantified from 3D rendered MPM images, and fiber orientation was measured in projected stacks of images. Collagen recruitment was observed to initiate at a finite strain, corresponding to a sharp increase in the measured mechanical stiffness, confirming the previous hypothesis and motivating the development of a new constitutive model to capture this response.Previous constitutive equations for the arterial wall have modeled the collagen contribution with either abrupt recruitment at zero strain, abrupt recruitment at finite strain or as gradual recruitment beginning at infinitesimal strain. Based on our experimental data, a new combined constitutive model was presented in which fiber recruitment begins at a finite strain with activation stretch represented by a probability distribution function. By directly including this recruitment data, the collagen contribution was modeled using a simple Neo-Hookean equation. As a result, only two phenomenological material constants were required from the fit to the stress stretch data. Three other models for the arterial wall were then compared with these results. The approach taken here was successful in combining stress–strain analysis with simultaneous microstructural imaging of collagen recruitment and orientation, providing a new approach by which underlying fiber architecture may be quantified and included in constitutive equations.

Effect of anisotropy, kinematic hardening, and strain-rate sensitivity on the predicted axial crush response of hydroformed aluminium alloy tubes

There exists considerable motivation to reduce vehicle weight through the adoption of lightweight materials while maintaining energy absorption and component integrity under crash conditions. Aluminium and magnesium alloys, advanced high-strength steels, and composites are all proposed candidates for replacing mild steel in automotive structures. It was of particular interest to study the crash behaviour of lightweight tubular hydroformed structures. Thus, the current research has studied the dynamic crush response of hydroformed Al–Mg–Mn aluminium alloy tubes using both experimental and numerical methods. The research focused on axial crush structures that are designed to absorb crash energy by progressive axial folding. The main experimental parameter that was varied during the hydroforming process was the corner-fill radius of the tube. Numerical studies were carried out using explicit dynamic finite element models incorporating advanced constitutive material models to capture the measured forming and crash history. A constitutive model was implemented in the finite element models combining the Johnson–Cook strain-rate sensitivity model, a non-linear isotropic-kinematic hardening model, and the Yld2000-2d anisotropic model. Each effect was isolated, and it was shown that strain-rate sensitivity slightly increased the energy absorption capabilities while kinematic hardening and anisotropy effects decreased the energy absorption capabilities during axial crush. When including all three effects, the predicted energy absorption was less than the response predicted from simulations performed using the von Mises yield criterion and in reasonable agreement with measured data. It is recommended that a combined constitutive model be utilized for the study of materials that show sensitivity to the Bauschinger effect, strain-rate effects, and anisotropy.

Influences affecting the soil-water characteristic curve

The soil-water characteristic curve (SWCC) is the primary partially saturated soil information as its behavior and properties can be derived from it. Although there have been many studies of unsaturated soils and the SWCC, there is still no combined constitutive model that can simulate soil characteristics accurately. In cases when hydraulic hysteresis is dominant (e.g. under cyclic loading) it is particularly important to use the SWCC. In the past decades, several mathematical expressions have been proposed to model the curve. There are various influences on the SWCC as a source of information, so the curves obtained from conventional tests often cannot be directly applied; and the mathematical expressions from one scenario cannot be used to simulate another situation. The effects of void ratio, initial water content, stress state and high suction were studied in this work revealing that water content and stress state are more important than the other effects; but that the influences tend to decrease when suction increases. The van Genuchten model was modified to simulate better the changes in the degree of saturation at low values of suction. Predictions were compared with experimental results to determine the simulation capability of the model.

Combined Model of Strain-Induced Phase Transformation and Orthotropic Damage in Ductile Materials at Cryogenic Temperatures

Ductile materials (like stainless steel or copper) show at cryogenic temperatures three principal phenomena: serrated yielding (discontinuous in terms of dσ/dε), plastic strain-induced phase transformations and evolution of ductile damage. The present paper deals exclusively with the two latter cases. Thus, it is assumed that the plastic flow is perfectly smooth. Both in the case of damage evolution and for the 0 phase transformation, the principal mechanism is related to the formation of plastic strain fields. In the constitutive modeling of both phenomena, a crucial role is played by the accumulated plastic strain, expressed by the Odqvist parameter p. Following the general trends, both in the literature concerning the phase transformation and the ductile damage, it is assumed that the rate of transformation and the rate of damage are proportional to the accumulated plastic strain rate. The 0 phase transformation converts the initially homogenous material to a two-phase heterogeneous ”composite”. The kinetics of phase transformation is described by the relevant linearized law of evolution of the volume fraction of 0 martensite in the austenitic matrix [Garion, C. and Skoczen, B. (2002a). The evolution of orthotropic damage is characterized by the fact that the principal directions of damage are generally not colinear with the principal directions of stress. The damage rate tensor depends linearly on the strain energy density release rate tensor (conjugate force) and on the material properties tensor C, that reflects the orthotropy level. The relevant kinetic law of damage evolution and the combined constitutive model, including phase transformation, are developed in the present paper. The model is particularly suitable to describe the evolution of highly localized damage fields in thin-walled shells, subjected at cryogenic temperatures to the loads far beyond the yield point. It has been applied to the prediction of the response of the bellows expansion joints (corrugated thin-walled shells) designed for the inter-connections of the Large Hadron Collider at CERN.