Elastic-plastic Constitutive Model Research Articles

Deformation Behavior of Superalloy Powder Compact under Hot Isostatic Pressing

Herein, the deformation behavior of a superalloy powder compact under hot isostatic pressing (HIP) is investigated by implementing an elastic–plastic constitutive model into the finite element analysis software MSC Marc. The coefficients of the constitutive model are obtained from interrupted HIP experiments. Finite element calculation results for the shape change of the powder compact under HIP agree well with the experimental results. Isothermal HIP and containerless HIP, both of which are based on finite element simulations, are conducted to study the dependence of the deformation on the container and temperature gradient. The stress state in all of the regions in the powder body deviates from the isostatic state of the compact even under isostatic pressing, due to the introduction of von Mises stress under the strong influence of the container. The temperature gradient is affected by the characteristic thermal conductivity and specific heat capacity of the porous powder body and container. Nonuniform temperature and stress distribution result in nonuniform densification, which eventually results in uneven powder compact shrinkage.

SPH Simulation of Structures Impacted by Tailing Debris Flow and Its Application to the Buffering Effect Analysis of Debris Checking Dams

Since the tailing dam fails catastrophically with substantial instantaneous deformation, it is difficult to measure the migration of debris flow caused by the failure of the tailings dam. A simulation model of tailing debris flow based on Smoothed Particle Hydrodynamics (SPH) theory of elastic-plastic constitutive equation has been established by considering the viscoplasticity of mud and the elastic-plastic characteristics of tailing sand to investigate the impact effect of tailing flow on the downstream structures. By comparing the experimental and two different simulation results obtained, it can be concluded that SPH elastic-plastic constitutive model can effectively simulate the accumulation and migration processes of the tailing debris flow, which indicates that the SPH model has good applicability to solve geotechnical large deformation problems of similar tailings flow slide. Then, the verified simulation model developed based on a series of simulations of tailing debris flow propagations was used to determine the momentum reduction on the downstream structure resulting from the presence of a simple checking dam perpendicular to the direction of propagation and to determine the characteristics of stresses applied to this structure in terms of peak impact force and evolution over time to the main flow direction.

Bending induced wrinkling and creasing in axially crushed aluminum tubes

Concertina folding of tubes used for impact mitigation bends the tube section to tight curvatures that can lead to failures on the tensioned side of the folds. This paper reports results from such axial crushing experiments on Al-6061-T6 circular tubes in which cleft-like features were also observed on the compressed sides of folds. Microscopic examination of the compressed sides of sectioned folds at different stages of bending revealed the following. Compression leads to surface wrinkles that are initiated by small initial surface roughness. Further bending increases the amplitude of the wrinkles, and at even higher bending the wrinkles morph into folds, creases, and sharp discontinuities. Metallographic examination of these surface undulations revealed that surface wrinkles encompass several grains, which deform conforming to the imposed local geometric changes. With this in mind, the axial crushing was simulated at the continuum level via an axisymmetric finite element analysis coupled with a suitably calibrated non-quadratic elastic–plastic constitutive model. A sufficiently refined mesh and representative initial surface imperfections enabled monitoring of the evolution of surface instabilities on the compressed sides of folds. Surface wrinkles appear at compressive strains of about 50%. As the local bending increases, their amplitude grows, and subsequently they evolve into local folds, and creases that resemble surface features observed in the experiments.

Fracture mechanics testing and crack propagation modelling in polypropylene pipes

PurposeThe main aim of this study is to determine the fracture toughness and accordingly to predict the fracture initiation, crack propagation and mode of crack extension accurately in polypropylene subsea pipes subjected to internal pressure.Design/methodology/approachTensile test was performed following the ISO 527–1 standard. An elastic-plastic constitutive model was developed based on the tensile test results, and it is implemented in the FEA model to describe the constitutive behaviour of the polypropylene material. Three-point bend tests with linear-elastic fracture mechanics (LEFM) approach were conducted following ISO-13586 standard, from which the average fracture toughness of the polypropylene pipe material in crack-opening mode was found as KIc = 3.3 MPa√m. A numerical model of the experiments is developed based on the extended finite element method (XFEM), which showed markedly good agreement with the experimental results.FindingsThe validated XFEM modelling approach is utilised to illustrate its capabilities in predicting fracture initiation and crack propagation in a polypropylene subsea pipe subjected to an internal pressure containing a semi-elliptical surface crack, which agrees well with existing analytical solutions. The XFEM model is capable of predicting the crack initiation and propagation in the polypropylene pipe up to the event of leakage.Originality/valueThe methodology proposed herein can be utilised to assess the structural integrity and resistance to fracture of subsea plastic pipes subjected to operational loads (e.g. internal pressure).

Experimental and numerical study on the mechanical properties of cortical and spongy cranial bone of 8-week-old porcines at different strain rates.

Pediatric porcines have widely been used as substitute for children in biomechanical research. Previous studies have used entire piglet cranium when testing their properties. Here, the piglet craniums from the frontal and parietal locations were carefully dissected into spongy and cortical part, and tensile tests at different strain rates were then conducted on these two bone types. It is found that the elastic modulus, yield stress, and ultimate stress of the cortical bone were all significantly higher than those of the spongy bone. The ultimate strains of the cortical and spongy bone were similar. Overall, the effect of the position on the mechanical properties did not reach significance. Cortical bone strength from the frontal location was slightly higher than that obtained from the parietal location; however, spongy bone did not show this location difference. The mechanical properties of both the cortical and spongy bone are significantly strain-rate dependent. Specifically, the elastic modulus, yield stress, and the ultimate stress of the cortical bone increased by approximately 123%, 63%, and 50%, respectively, with strain rates ranging from 0.001 to 10/s. For spongy bone, increases were approximately 128%, 73%, and 77%, respectively. Ultimate strain decreased by approximately 37% and 7% for cortical and spongy bone, respectively. An elastic-plastic constitutive model incorporating with strain rate based on a combined exponential and logarithmic function was proposed and implemented into LS-DYNA through user-defined material. The developed model and the subroutine code successfully simulated the strain-rate characteristics and the fracture process of the bone samples.

Experimental Study on Stress Paths of Unsaturated Soils

The distribution of loess in China is concentrated in the Midwest, which is a typical structural soil. Its structure is extremely special, and its sensitivity to water is also unique. The strength and deformation characteristics of this kind of unsaturated soil have a great influence on the stress it bears. This study starts with the same stress ratio loading of loess with different moisture content and corresponding remolded loess, aiming at the changes of the structure of unsaturated soil under different stress ratios. Based on the comprehensive analysis of structural potential parameters of unsaturated soil under the condition of poor stress, the appropriate hardening parameters are constructed, and the corresponding elastic-plastic constitutive model is established. At first, the corresponding test scheme is designed, and then the test results are analyzed. Finally, the specific analysis is carried out from the constitutive model of stress elastic-plasticity of unsaturated soils.

Effect of feed condition on thrust force and torque during continuous and step-by-step drilling of cortical bone

Abstract Chip evacuation is one of the fundamental difficulties during continuous drilling of the cortical bone. As the drilling process progresses, discontinuous chips tend to cluster together and clog the drill flutes, which can result in increased temperature, poor hole quality, elevated thrust force and torque, and can even cause the drill bit to break. In this study, continuous and step-by-step drilling processes of the cortical bone were conducted to investigate the thrust force and torque using experimental and numerical modeling methods. By using the finite element method, an elastic–plastic constitutive model was employed to predict the thrust force and torque experienced during bone drilling, and a series of drilling tests was conducted. The experimental results showed a significant increase in the thrust force and torque owing to the chip clogging during the continuous drilling process while this increase was not observed in the simulations. It was shown that the step-by-step drilling method can reduce the increased thrust force and torque during the drilling of cortical bone, and the numerical results of this drilling process were demonstrated to be consistent with the experimental ones. The reduced thrust force and torque indicated that the chip clogging may be reduced by using the step-by-step drilling method, and the numerical results suggested that the finite element model can be used to assist surgeons in selecting drilling conditions to control the process in step-by-step drilling of the cortical bone.

Efficacy of elastic-plastic constitutive models in predicting the geo-mechanical response of gas hydrate sediments

Efficacy of elastic-plastic constitutive models in predicting the geo-mechanical response of gas hydrate sediments

Equivalent seismic coefficients for caisson foundations supporting bridge piers

Safety of a foundation under seismic loading is strongly dependent on the inertial forces transmitted by the superstructure, exchanged with the surrounding soil and acting into the foundation itself. The latter contribution, typically neglected for shallow and pile foundations, should be considered for caisson foundations, much more massive and rigid than the foundation soil. In this paper, the inertial forces acting in caisson foundations during seismic shaking are extracted from the results of a parametric study where different caissons supporting bridge piers are subjected to severe ground motions. The parametric study was carried out in the time domain via 3D Finite Element (FE) dynamic analyses performed in terms of effective stresses but assuming an undrained response of the foundation soil. Non-linear and inelastic soil behaviour was described in the analyses by an elastic-plastic constitutive model with isotropic hardening.In the framework of a pseudo-static approach, the caisson inertia is represented by equivalent horizontal and rotational seismic coefficients, kh eq and krot eq, relating the generalised inertial forces to the caisson weight. The coefficient kh eq turns out to be always remarkably smaller than the maximum value computed at ground surface in free-field conditions, kh max(g.s.). The equivalent seismic coefficients kh eq and krot eq are expressed via empirical relationships as a function of the dynamic properties of the whole system and the seismic input, through dimensionless parameters. Calculation examples are finally given, where safety assessment of bearing capacity is made for different systems using the pseudo-static approach, showing that use of the seismic coefficients computed by the proposed relationships yields results consistent with the ones obtained from the dynamic analyses.

An analytical solution for circular tunnels excavated in rock masses exhibiting viscous elastic-plastic behavior

Investigating time-dependent behavior of tunnels driven in rocks has been the topic of interest for many years. The majority of researches were conducted with the assumption that the behavior of the surrounding rock masses is viscoelastic. In this paper, an analytical solution is proposed for circular tunnels under hydrostatic stress field, whose surrounding rock mass is isotropic, homogenous, obeying viscous elastic-plastic constitutive model. It is assumed that the rate of excavation is infinitely large. Therefore, the solution is proposed for unlined tunnels when the advance of tunnel face is halted, or after lining installation when the tunnel face is far from the studied section. The results were compared with those predicted by finite difference numerical model which exhibited a good agreement for both lined and unlined tunnels, except for large times where numerical model results slightly exceed the values predicted by the proposed solutions for lined tunnels.

Modeling the effects of loading scenario and thermal expansion coefficient on potential failure of cryo-compressed hydrogen vessels

A multiscale thermomechanical model for a simplified Type-3 cryogenic, compressed-hydrogen (H2) storage vessel is described in this paper. The model accounts for the temperature-dependent elastic-plastic behavior of the vessel's carbon/epoxy composite overwrap and aluminum alloy liner. The homogenized thermo-elastic-plastic behavior for the individual laminae of the vessel layup is obtained using an incremental Eshelby-Mori-Tanaka approach associated with a micromechanical failure criterion to predict laminar failure while a standard elastic-plastic constitutive model is used to describe the behavior of the typical aluminum alloy assumed for the liner. The vessel's response to external loadings is modeled using a finite element method. Four loading scenarios, representing four thermomechanical cycles applied to the vessel, are analyzed to evaluate constituent and laminar stresses as well as the associated failure criterion during the cycle according to these scenarios. The model can provide helpful guidance to mitigate thermal stresses by selecting a suitable loading scenario, optimizing the layup, and tailoring the thermomechanical properties of the resin matrix.

A damage constitutive model and its characterization parameters identification for elastic-plastic materials

This paper proposes a simple damage constitutive model for elastic-plastic materials on the basis of the classical elastic-plastic constitutive model and damage mechanics theory. Based on the simple damage constitutive model, ABAQUS built-in Python software was used to develop the virtual experimental platform, and the whole process simulation of the specimens stretching until the fracture was carried out. The correspondence between the damage characterization parameters and the performance indexes such as the fracture strain and the percentage reduction of area was studied. According to the comparison of the virtual/real test results of ZL114A, the situation shows that the simple damage constitutive model can realize the high fidelity simulation of the damage behavior of elastic-plastic materials. The relative accuracy of the important material property parameters such as the ultimate strength, the percentage total elongation at fracture and the percentage reduction of area reaches 5%.

A damage coupled elastic-plastic constitutive model and its application on low cycle fatigue life prediction of turbine blade

Based on continuum damage mechanics (CDM), a damage coupled elastic-plastic constitutive model combined with multilinear hardening relation is proposed and applied on low cycle fatigue (LCF) life prediction of turbine blade. The model has considered the local rigidity attenuation of structure caused by fatigue damage in elastic and plastic stage, and it is implemented combining with finite element method (FEM) to predict the crack initiation lives of turbine blades. Runge-Kutta (RK) method is employed in the solving process of damage accumulation. By conducting the calculation in several time step sizes, the convergence of the proposed model is examined. To validate the predicted results, groups of LCF experiments are conducted on full-scale turbine blades. The macroscopic fracture shows that the crack initiation region is in accordance with the predicted results. Compared with the experimental results, the predicted lives of the proposed model, an existing CDM model without coupling with constitutive relation and Morrow model are within factors of 2.31, 3.93 and 9.15 in scatter band respectively, indicating the high accuracy of the proposed model. Expect for turbine blades, the proposed model can be used to predict the LCF lives of other structures.

FE analysis of the residual stresses for the laser welded T-joint of Al-Li alloy under service loads

This paper attempts to reveal the evolution of welding residual stresses (WRS) in skin-stringer structure of Al-Li alloy exposed to service loads. 3D thermal-structural finite element (FE) formulation of the dual laser-beam bilateral synchronous welding process is first derived, and its accuracy is verified by experimental tests to acquire accurate WRS. FE numerical analyses incorporated with the elastic-plastic constitutive model, taking the WRS, strains distribution and total equivalent plastic strains as an initial condition, are next carried out to explore the residual stresses redistribution of the T-joint under service loads. The results unveil that longitudinal stress relaxation is pronounced (especially at the weld) in the skin after the end of the loads applying. However, the longitudinal stress in the middle of the stringer is not sensitive to the service loads. The extended high tensile stress concentration zone inside the joint in case 2 and case 4 may be the potential failure location after the progressive loading of the skin-stringer welding structure. Additionally, the weld toe, which is the obvious stress sudden change zone in the service process, is a non-negligible position for the improved failure estimation of the aerospace skin-stringer structure.

Flexural behavior of corroded HPS beams

Experimental research is conducted to investigate the flexural behavior of corroded High Performance Steel (HPS) beams. Four beams with various corrosion damage are designed and subjected to electrochemical accelerated corrosion process. 3D scanning technology is employed to analyze the geometric features affected by the corrosion damage. Flexural tests are carried out, and the impact of corrosion on the flexural response is discussed. Considering the randomness of corrosion pits in each area, predictive models are proposed for the flexural strength of corroded beams with an idealized elastic-plastic and linear-hardening constitutive relationship model. An analysis comparing the proposed models with Chinese and American codes is made. Results show that increasing the corrosion damage leads to a decrease of discreteness in the residual sectional area and causes a transformation in the compressed flange from noncompact to slender. A corrosion loss less than 10% leads to slight deterioration of both strength and stiffness degradation, while further corrosion damage results in a significant decrease. The depth and length of the buckling wavelength for corroded beams decreases gradually as the corrosion damage become more serious. The analytical models IEM and LHM or the GB50017-2017 may be suitable for predicting the lower and upper limit values of the ultimate flexural moment, respectively, and results predicted by AISC are conservative.

Characterisation and constitutive modelling of biaxially stretched poly(L-lactic acid) sheet for application in coronary stents

A poly(L-lactic acid) stent is exposed to a variety of processing techniques, temperatures and environmental conditions during its lifecycle, from the manufacturing process, to crimping through to deployment within the body. The effect of the biaxial stretching procedure and the effects of temperature and extension rate (post-processing) on the mechanical response of poly(L-lactic acid) are hereby investigated, and a constitutive model calibrated against experimental data is proposed. Dumb-bell specimens were punched from biaxially stretched sheets subjected to different processing histories, and tested under uniaxial tension at various temperatures (20, 37 and 55 °C) and extension rates (1, 5 and 10 mm/min). A Design of Experiments methodology was employed to identify the parameters that had the most significant effect on the mechanical response of the polymer. Results show that the elastic modulus and yield strength of the stretched sheets are strongly dependent on the aspect ratio of the biaxial deformation, along with the temperature during uniaxial deformation (post-processing). In contrast, these mechanical properties were not heavily dependent on extension rate (post-processing). A transversely isotropic, elastic-plastic constitutive model for finite element implementation is proposed, with the intention that it may be used as a design tool for developing high stiffness, thin-strut polymeric stents that contend with the performance of their metallic counterparts.

A new method of developing elastic-plastic-viscous constitutive model for clays

A new method is presented to develop the existing elastic-plastic constitutive model into an elastic-plastic-viscous one for clays. The actual loading process is divided into an instant process and a delayed process denoting the elastic-plastic strain and viscous strain, respectively. The elastic-plastic strain is determined by either an elastic-plastic model for overconsolidated clays or an improved model based on the elastic-plastic model for normally consolidated clays. In order to calculate viscous strain, a reference state line is defined based on the actual loading path. Combining the reference state line, an existing elastic-plastic model can be conveniently developed into an elastic-plastic-viscous model. Furthermore, using the proposed method, the modified cam clay model is extended into an elastic-plastic-viscous model. Comparisons with test results demonstrate that the extended model can capture the main time-dependent behaviours of clays, including creep, stress relaxation and strain rate effects.

An Elastic-plastic Constitutive Model of Concrete Based on Thermodynamic Principles and Its Application in Arch Dam Design

An Elastic-plastic Constitutive Model of Concrete Based on Thermodynamic Principles and Its Application in Arch Dam Design

Analysis of the fatigue crack initiation of a wind turbine gear considering load sequence effect

Under the action of the wind, wind turbine gears experience complex loading histories in which the amplitude of the load is varying. The variable load conditions make the load sequence and the load amplitude inverse number as important factors to be considered for gear fatigue analysis. In the present work, a damage-coupled elastic-plastic constitutive model based on the continuous damage mechanics (CDM) is established to analyze the influence of load sequence on rolling contact fatigue (RCF) crack initiation of a wind turbine gear. The crack initiation is indicated by reaching the critical threshold of the defined damage variable related to the shear stress range and the plastic strain. During repeated loading cycles, the deterioration of material is reflected by gradually reducing mechanical properties. The numerical simulation is carried out in the frame of ABAQUS using the subroutine of user defined material subroutine (UMAT). The two-level load conditions are selected and results of which are compared with those of constant amplitude load conditions. Different inverse numbers are utilized to investigate the influence of load amplitude inverse number on crack initiation life. Simulation results are compared with existing damage accumulation criteria. The results indicate that when the first crack initiates, the sum of lifetime ratio is greater than unity for the low-high load sequence, while this value is less than unity for the high-low load sequence. Furthermore, the increase of the load amplitude inverse number will weaken the influence of the load sequence with regard to the crack initiation life. The highly nonlinear characteristic of damage accumulation during fatigue process under variable loading histories is captured by the proposed method. This method provides a new way to reveal the contact fatigue process of gears under variable loading histories and lay a foundation for predicting the accurate fatigue life under the real, complex loading condition of a gear.

A finite-strain phase-field approach to ductile failure of frictional materials

This work presents a modeling framework for the ductile failure of frictional materials undergoing large deformations with a focus on soil mechanics. Crack formation and propagation in soil can be modeled in a convenient way by the recently developed continuum phase-field approach to fracture. Within this approach sharp crack discontinuities are regularized. It allows the use of standard discretization methods for crack discontinuities and is able to account for complex crack paths. In the present contribution, we develop a computational modeling framework for the phase-field approach to ductile fracture in frictional materials. It combines a non-associative Drucker–Prager-type elastic-plastic constitutive model with an evolution equation for the crack phase field in terms of an elastic-plastic energy density. An important aspect is the development of an isotropic hardening mechanism that accounts for both friction and cohesion hardening. In order to guarantee a locking- and hourglass-free response, a modified enhanced element formulation, namely the consistent-gradient formulation, is employed as a key feature of the finite-element implementation. The performance of the formulation is demonstrated by means of representative numerical examples that describe soil crack formation rooted in elastic-plastic fracture mechanics.