Constitutive Model Constants Research Articles

Estimation of johnson-cook constitutive model constants from sheppard and jockson model

This work introduces a novel approach for determining the material constants of the Johnson Cook constitutive model, which is used to estimate flow stress when a material is open to higher strain rates, stresses, and temperatures. In this study the material characteristics/constants of the Johnson-Cook constitutive model were derived by using another flow stress model which was introduced by Sheppard and Jackson. The input data was collected from published hot compression test results. This method can potentially reduce the experimental efforts required for evaluating the data of the Johnson-Cook model. In this work aluminum alloys 7075-T65I and Ti- 6Al-4V have been considered for analysis. These materials have their mechanical properties at high temperatures and are of excellent significance for new manufacturing procedures that use deformation to produce a bonding in the solid state, such as friction stir welding and magnetic impulse welding. The flow stress variation of the two models and similar characteristics have been observed at some points over the temperature range. The strain rate constant (c ) and temperature softening coefficient (m) for each material have been determined and results were compared with experimental data which were found in the literature. By adopting this method it is possible to eliminate torsion test to know the strain rate effect on a material. These data could also be used to simulate possibly the best processes as forging, rolling at higher temperatures, and creep.

Hot Compression Deformation Characteristics of Nimonic Alloy as-forged

Hot Deformation Behavior and Constitutive Model of the nickel-base alloy Nimonic Alloy as–forged are investigated by hot compression tests in the ranges of strain rate (0.001-1s−1) and temperature 1323-1423K, at intervals 50K. During the process of compression deformation, with the increase of true strain, the flow stress first increases rapidly to the peak value. Then, the flow stress decreases with the increase of true strain. Flow curves show dynamic recrystallization occurs at low strain rate (0.001-0.1 s−1) and temperature (1323-1423K). The softening mechanism at high strain rate (1 s−1) is dynamic recovery. According to the values of the ture stress and strain, the material constants of constitutive model are calculated and Arrhenius-type equation is given.

Determination of Constitutive Material Model Constants for Ti6Al4V Alloy at Near Orthogonal Machining Conditions

Abstract The accuracy of numerical modeling of a machining process largely depends on material model constants. The Johnson-Cook (J-C) material model constants, i.e., A, B, C, n, and m, describe deformation behavior of material under thermomechanical loading. This paper considers an equivalent strain hardening exponent neq in place of ‘n’ in the J-C constitutive law for accurate prediction of material model constants at near orthogonal machining conditions. The effect of strain on the secondary deformation zone, i.e., the tool-chip interface, is also considered for accurate prediction of material parameters. In the present work, a machining approach based on response surface methodology and particle swarm optimization technique are used to identify J-C material model constants for the Ti6Al4V alloy. The cutting force, feed force, and chip thickness obtained from orthogonal experiments are used to evaluate the physical quantities of Oxley’s extension theory at different rake angles. It is noted that J-C constants determined from the present approach at a 7° rake angle are more accurate in predicting flow stress than J-C constants determined from other methods. J-C constants identified from a machining approach show less deviation from the measured equivalent flow stresses obtained at similar machining conditions.

The modification of steel belt layer of airless tire for finite element analysis

The airless tire can be considered as composite structure since it composed of several components with different materials for desired performance. The three main components of airless tire are rubber tread, shear band and polymer spokes. The shear band composed of three complex steel belt layers and should be considered as a sub composite structure. The finite element method can be used in designing and development of airless tire. However the diversity of materials in each component including the complex sub structure resulted in complicate modelling and consuming analysis time. Thus, the large computational resources are required to analyse those components. In this research, the simplification of modelling and analysis of airless tire was attempted by modification of steel belt layers. The Mooney-Rivlin hyperelastic model was used to describe the material properties of tread and spoke. The constitutive model constants were obtained by tensile and compressive test according to ASTM D412 and D575 standards, respectively. The simplified belt, which was developed by homogenization approach, was integrated into shear band component. The airless tire model with modified steel belt layers can be used to reduce the model complexity and analysis time while yields accurate results.

Predicting the Johnson Cook constitutive model constants using temperature rise distribution in plane strain machining

Johnson-Cook (JC) constitutive material model is the most common, yet simplest, model to describe the material behavior in machining that involves high strain and high strain rates accompanied with high temperature rise. Many studies have tried to predict JC model constants using computational and analytical procedures. However, these approaches are limited by computational costs and experimental restrictions. In this study, an original approach to determine the JC material model constants is proposed using the effects imposed by strain hardening, strain rate hardening, and thermal softening. An analytical approach is established upon the chip formation model in orthogonal cutting—plane strain machining—where the JC model is applied to calculate cutting energy due to plasticity and friction which ultimately involves temperature rise. Temperature is calculated at primary shear zone and secondary deformation zone using Oxley and modified Hahn’s models, which are dependent on material behavior and five JC constants. JC constants are calculated by performing a multi-objective optimization algorithm that searches for the minimum differences between the calculated temperature in the chip and the experimental results of temperature for different cutting conditions. The obtained JC constants are compared with the literature and close agreements are achieved. The appeal of the proposed methodology is in its low computational time, low experimental complexity, and low mathematical complexity. Finally, JC constants were used in finite element simulation of PSM to verify the model’s robustness and accuracy via comparing the cutting force, temperature distribution, and subgrain size of the chip for different cutting conditions.

Predictive Modeling of Machining Temperatures with Force⁻Temperature Correlation Using Cutting Mechanics and Constitutive Relation.

Elevated temperature in the machining process is detrimental to cutting tools—a result of the effect of thermal softening and material diffusion. Material diffusion also deteriorates the quality of the machined part. Measuring or predicting machining temperatures is important for the optimization of the machining process, but experimental temperature measurement is difficult and inconvenient because of the complex contact phenomena between tools and workpieces, and because of restricted accessibility during the machining process. This paper presents an original analytical model for fast prediction of machining temperatures at two deformation zones in orthogonal cutting, namely the primary shear zone and the tool–chip interface. Temperatures were predicted based on a correlation between force and temperature using the mechanics of the cutting process and material constitutive relation. Minimization of the differences between calculated material flow stresses using a mechanics model and a constitutive model yielded an estimate of machining temperatures. Experimental forces, cutting condition parameters, and constitutive model constants were inputs, while machining forces were easily measurable by a piezoelectric dynamometer. Machining temperatures of AISI 1045 steel were predicted under various cutting conditions to demonstrate the predictive capability of each presented model. Close agreements were observed by verifying them against documented values in the literature. The influence of model inputs and computational efficiency were further investigated. The presented model has high computational efficiency that allows real-time prediction and low experimental complexity, considering the easily measurable input variables.

Determining Al6063 constitutive model for cutting simulation by inverse identification method

Numerical simulation is an important method to investigate the cutting process due to its unmatched capability in discovering the cutting parameters including cutting force, distribution of stress and temperature, chip and surface formation mechanism. So its application has covered a wide range of materials from metallic, non-metallic to composite materials, and among the simulation of composite materials such as silicon carbide reinforced aluminum matrix composites (SiCp/Al) receives a great amount of attention. However, at present, the simulation is always faced with the deficiency of material constitutive model, which can more accurately describe the variation of the flow stress, e.g., the microstructure-based simulation of composites. In order to build a solid foundation for the microstructure-based simulation of SiCp/Al6063, this paper attempts to identify the constants of Johnson-Cook constitutive model for the matrix Al6063 by an inverse identification method based on the quasi-static compression, orthogonal cutting tests, and cutting simulation. And the established model is verified by the cutting experiments in terms of the cutting force and chip thickness. The applicability and advantages of inverse identification method is presented by the discussion on the problem of negative strain rate in using conventional approach.

Identification of plasticity constants from orthogonal cutting and inverse analysis

The aim of this work is that from experimental determined cutting process parameters be able to predict the plasticity input constants to Finite Element Method (FEM) models. In the present study the Johnson–Cook constitutive model constants are determined on the basis of cutting process parameters in orthogonal cutting and by use of inverse analysis. Previously established links between Johnson–Cook constitutive model constants and cutting process parameters in the cutting process such as primary cutting force and chip compression ratio is used serve as a starting point in the inverse analysis. As a reference material AISI 4140 has been chosen in this study, which is a tempered steel. The Johnson–Cook constitutive model constants in the reference material are being changed within an interval of ±30%. The inverse analysis is performed using a Kalman filter. The material model for the reference material is validated on the basis of the experimental results in previous work. The model showed to predict the cutting process parameters with a high level of accuracy. The predicted Johnson–Cook constitutive model constants in the present study achieve an error between simulated- and experimental cutting process parameters of maximum 2%. The method described in this study is not limited to identify Johnson–Cook constitutive model constants, but the method can also be used for other constitutive models. The same applies to the process itself and the selected cutting process parameters, but orthogonal cutting has been used to illustrate and validate this method.

Application and Analysis of Plane Woven C/SiC Composites Based on Continuum Damage Mechanics

The aim of this article was to propose a macroscopic damage model, which describes the nonlinear behavior observed on woven C/SiC ceramic matrix composites. The model was built within a thermodynamic framework with internal variables. The anisotropic damage evolution processes of the material were described by nonlinear damage isotropic and kinematic hardening functions in this model. The anisotropic damage and damage coupling were considered with a damage yield function including anisotropic coefficients. Using the principle of energy equivalence, the damage variables were defined by the unloading modulus and initial modulus. The damage variable and the irrecoverable strain induced by micro-crack propagation were deduced by thermodynamics. The constants of constitutive model were identified and the damage evolution processes under tensile and shear loading. Uniaxial tension and shear tests had been used to valid the constitutive model to C/SiC composites.

Damage Theoretical Analysis of 2.5D C/SiC Composites under Tensile and Shear Loading

An anisotropic damage constitutive model is developed to describe the damage behavior of C/SiC composites. Different kinematic and isotropic hardening functions were employed in damage yield function to describe accurately the damage nonlinear hardening. The damage variable is defined by the principle of energy equivalence. The degradation of stiffness and the unrecoverable deformation induced by micro-crack propagation were considered in this model. The constants of constitutive model are identified and the damage evolution processes under tensile and shear loading. Uniaxial tension and shear tests have been used to valid the constitutive model to C/SiC composites.

Characterization and evaluation of boron carbide for plate-impact conditions

This article addresses the response of boron carbide (B4C) to high-velocity impact. The authors previously characterized this material in 1999, using the Johnson-Holmquist [AIP Conf. Proc. 309, 981 (1994)] (JH-2) model. Since then, there have been additional experimental data presented in the literature that better describe the hydrostatic pressure (including a phase change). In addition, a series of plate-impact experiments (one-dimensional, uniaxial strain) that used configurations that produced either a shock, a shock release, or a shock reshock was performed. These experiments provide material behavior regarding the damage, failed strength, and hydrostat for which previously there has been little or no data. Constitutive model constants were obtained for the Johnson-Holmquist-Beissel [J. Appl. Phys. 94, 1639 (2003)] model using some of these plate-impact experiments. Computations of all the experiments were performed and analyzed to better understand the material response. The analysis provided the following findings: (1) The material fails and loses strength when the Hugoniot elastic limit (HEL) is exceeded. (2) The material has significant strength after failure and gradually increases as the pressure increases. (3) The shear modulus does not degrade when the material fails (as has been postulated), but rather increases. (4) When the material is reloaded from an initial shocked (failed) state, the loading appears to be elastic, indicating the material is not on the yield surface after failure. To provide more insight into the behavior of B4C, the strength versus pressure response was compared to that of silicon carbide (SiC). The strength of SiC increases as the pressure increases beyond the HEL, probably due to pressure hardening or strain hardening. It appears that B4C does not experience any hardening effects and fails at the HEL. Although the HEL for B4C is higher than that of SiC, the hardening ability of SiC produces a similar maximum strength with more ductility. Another important issue with B4C is that there are significant differences between plate-impact data reported by different researchers. These differences are due to one or more of the following possibilities: errors in obtaining the test data, errors in analyzing the test data, a high degree of scatter due to failure of the material, and/or the different manufactured forms of B4C simply behave as different materials. These differences also make it difficult to validate the model (constants) determined from one set of data by applying it to other data reported in the literature. Lastly, the model was used to simulate ballistic impact experiments over a large range of impact velocities (1500–4500m∕s). The computed results overpredict the penetration at low velocities and underpredict the penetration at high velocities. Future work will address this inconsistency, but until this issue is resolved, the current model and constants should be used with caution when applied to ballistic impact and penetration.

Strain-rate effects for high-strain-rate computations

This paper examines the effect of strain rates for computations involving high strain-rates, beyond 10 3 s -1 . Although it is generally agreed that there is an enhanced rate effect at these higher rates, there is uncertainty regarding the interpretation of dynamic test data, the form of the high-rate effect, and the effect of the high rates on practical problems of interest. This article provides an assessment of the high-rate effect for Taylor (cylinder impact) tests, a determination of high-rate constitutive model constants from the Taylor tests, and the effect of the high-rate response on penetration computations. The computations are performed with the Johnson-Cook constitutive model and an enhanced (high-rate) form of the Johnson-Cook model.

Investigation of fused silica dynamic behaviour

The survivability of the fused silica shields to shrapnel impacts is a key factor for the affordable operation of the intense laser irradiation future facility Laser Mega Joule (CEA-CESTA). This paper presents experimental data and computational modelling for LMJ fused silica upon shock wave loading and unloading. Gas-gun flyer plate impact and explosively driven tests have been conducted to investigate the dynamic behaviour of this material. Hugoniot states and the Hugoniot Elastic Limit of LMJ fused silica have been obtained. These experimental data are useful for determining some constitutive model constants of the Crack-Model, a continuum tensile and compressive failure model with friction based on Rubin M. B. and Attia A. V.'s work. This model has been improved by taking into account nonlinear elasticity. The numerical results obtained by performing computations of the previous tests and some ballistic impact tests are discussed. Further developments to simulate the permanent densification and the solid-to-solid phase transformation of fused silica are required.

A Phenomenological Constitutive Model Constructed for PC/ABS Blends

Based on previous available constitutive models, a phenomenological constitutive model has been constructed and is proposed to describe the strain, strain rate and temperature dependentdeformation behavior of PC/ABS blends. In this paper, four quasi-static uniaxial tension tests of a specimen tested at different strain rates and temperatures were used to identify the constitutive model constants. By using the proposed constitutive model, predicting the stress-strain behavior of the PC/ABS blend tested at certain strain rate and different temperatures compares well to the behavior exhibited from the tests. From comparison between the DSGZ and the proposed models, proposed model shows a better prediction. Evaluation of the proposed constitutive model was also presented and it has revealed that the proposed model might have a potential to be used for predicting a wide range of temperatures and high strain rates behavior of PC/ABS blends.

Application of three numerical procedures to evaluation of earthquake-induced damages

This paper presents and compares the applications of three numerical procedures, Shake, Dysac2 and Sumdes , to the evaluation of earthquake-induced damages. Shake, a total stress-based equivalent-linear procedure, and Dysac2, an effective stress-based, fully coupled, nonlinear, finite element method-based procedure, were applied to the evaluation of liquefaction-induced building damage in the San Francisco Marina District which occurred during the 1989 Loma Prieta earthquake. Sumdes , an effective stress-based, fully coupled, nonlinear, finite element method-based numerical procedure, was applied to the evaluation of liquefaction-induced deformation which occurred at the Port Island during the 1995 Kobe earthquake. Three sites in the Marina District were selected for this study and analyzed using numerical procedures Shake and DYSAC2. In-situ and laboratory tests were used to obtain the initial state parameters and constitutive model constants for the liquefaction-induced building damage analysis during the Loma Prieta earthquake. The results of this analysis are presented and compared with the observed behavior in the Marina District during the 1989 Loma Prieta earthquake. Differences between the predictions of the Dysac2 and Shake computer programs are discussed. The laboratory formation factor tests and shear wave velocity results were used to obtain the initial state parameters and constitutive model constants for the analysis of the liquefaction-induced deformation of an instrumented site at Port Island, Kobe. A summary of the results of the analyses performed using Sumdes are presented and compared with observed behaviors. Close agreements are shown to exist between the evaluated and observed results. The two effective stress-based numerical procedures, Dysac2 and Sumdes , were verified during the VELACS (Verification of Liquefaction Analysis using Centrifuge Studies) and VELACS-Extension projects.

Numerical Simulation of Liquefaction-Induced Deformations

The observed dynamic response of an instrumented site at Port Island during the 1995 Kobe earthquake was utilized to demonstrate the feasibility of computer simulation of earthquake-induced site response and liquefaction-induced deformations of a level ground site. Nondestructive in situ electrical and shear wave velocity methods were used to obtain the initial state parameters and constitutive model constants representative of the site. The analysis used the fully coupled, effective stress-based, nonlinear, finite-element program SUMDES with a reduced-order bounding surface hypoplasticity model to simulate the stress-strain behavior of cohesive soils and a modified reduced-order bounding surface hypoplasticity model to simulate the stress-strain behavior of noncohesive soils. The results of the dynamic analysis, such as acceleration time histories and liquefaction-induced deformations, agreed reasonably well with the acceleration time histories and liquefaction-induced vertical and horizontal deformation behaviors observed during the Kobe earthquake. The results of this study show that computer simulation of earthquake effects at level ground sites is possible using nondestructive in situ testing and a verified numerical procedure.

The viscoplastic behavior of hastelloy-X single crystal

A viscoplastic constitutive model for simulating the behavior of Hastelloy-X single crystal material was derived based on crystallographic slip theory. To determine the appropriate constitutive model constants and to test the predictions of the model, tests on Hastelloy-X crystals were carried out, including the rate sensitivity, cyclic hardening, nonproportional hardening, relaxation, and strain rate dip tests. It was found necessary to include cube slip in the model in order to correlate the uniaxial behavior of the single crystal, to incorporate the interaction effects in both the hardening and the dynamic recovery evolution equations for the drag stress, and to successfully capture correct strain rate sensitivity under biaxial tension-torsion loading conditions.

Evaluation of cylinder-impact test data for constitutive model constants

This paper examines the usefulness of cylinder-impact test data to determine constants for various computational constitutive models. The Johnson–Cook and Zerilli–Armstrong constitutive models are evaluated by comparing model predictions to tension, torsion, and cylinder-impact test data. Then the cylinder-impact test data are used to determine constitutive model constants for various forms of these models. Under bounded conditions of strains and strain rates, this approach can produce useful results. It can also produce very erroneous results if not used properly.

Scale-up Technique of Slurry Pipelines—Part 1: Turbulence Modeling

A kinetic energy turbulence model is proposed for the flow simulation and scale-up of slurry pipelines (in Part 1). The numerical integration is performed by using a modified finite volume technique with application to high convective, two-phase flows, in two and three dimensions (in Part 2 [1]). The mixture kinetic energy and eddy viscosity one-equation turbulence models are compared. The constitutive equations and model constants are tested using laboratory experiments and then employed for large-scale applications. The governing equations are derived from the space/time averaging of the momentum equations and integrated in the pipe cross section using the finite volume approach. The specific interaction stresses (liquid-liquid, liquid-solid, solid-solid and solid-wall) are expressed in the mathematical formulation. The predictions for the velocity and concentration distributions, as well as on the mean velocity-headloss correlations, have been compared to available experimental data (water-sand, water-glass, water-coal mixtures; of concentrations αS = 5 – 40 vol percent, in pipes of various diameters D = 40 – 500 mm). The suggested model can simulate multi-species particulate pipe flow for which the semiempirical methods cannot be satisfactorily applied. The numerical tests and comparison to experiments show the model capabilities to scale-up data from laboratory to real flow situations via infinitesimal two-phase flow analysis.