Work-hardening Model Research Articles

Effects of work hardening models on low-cycle fatigue evaluations of coiled tubing with CT-100 steel

In the present study, low-cycle fatigue life of a coiled tubing (CT) with a CT-100 steel was evaluated by using various work hardening models. Tensile and low-cycle fatigue tests were performed, and experimental results were used to calibrate material model constants. A nonlinear finite element model was constructed in the ABAQUS program by using a CT fatigue test machine. During the test cycles, bending and straightening conditions were repeated and histories of strains were collected. The multiaxial low-cycle fatigue life was calculated by using Manson–Coffin relation and Tresca criterion. The kinematic and combined hardening models can be used to evaluate the fatigue life of CT, and their results are conservative compared with the fatigue test results. Results of the present study can be used as the basic data in establishing CT fatigue analysis.

Effects of Heterogeneous Microstructures on the Strain Hardening Behaviors of Ferrite-Martensite Dual Phase Steel

The complex strain hardening behaviors of dual phase (DP) steel are subjected to the heterogeneous microstructures. The current work aims to predict the strain hardening behaviors of ferrite-martensite DP steel, focusing on the effects of heterogeneous microstructure on mechanical properties. The flow stress of material was calculated based on the dislocation-based work-hardening model with considering the multi-boundaries hardening. The ferrite-martensite phase boundary percent and grain shape factor were selected as the heterogeneous feature parameters, which were introduced into the new proposed model. The theoretical calculated stress-strain responses were verified with experimental results using the tensile test. The model with the boundary strengthening consideration has more accurate results. The parameter effects of ferrite-ferrite boundary (FFB) spacing, ferrite-martensite boundary (FMB) percent, and grain shape factor on the flow stress-strain curve were researched.

Unified modeling of work hardening and flow softening in two-phase titanium alloys considering microstructure evolution in thermomechanical processes

One of the most critical aspects in understanding the deformation behavior of two-phase titanium alloys subjected to thermomechanical processes (TMPs) lies in being able to describe the flow stress accurately. To this end, in this study, initially, hot tension tests were conducted on a two-phase Ti-6Al-2Zr-1Mo-1V alloy. It was observed that the flow stress at a given temperature and strain rate exhibits work hardening, followed by flow softening. Flow softening occurs at the peak strain, where the maximum stress is observed; peak strain decreases with increasing temperature and decreasing strain rate. Variations in peak strain are more obvious at low temperatures and high strain rates. Later, the microstructure of the alloy was analyzed and the results show that work hardening and flow softening are caused by dynamic recrystallization (DRX). The DRX volume fraction was found to exhibit an increasing trend and discontinuous dynamic recrystallization (DDRX) was observed at increasing temperature and decreasing strain rate. With respect to microstructure evolution, a unified model consisting of a thermally activated stress component and an athermal stress component was developed. In the athermal stress term, dislocation density and the Hall-Petch effect were used to describe the work-hardening and flow-softening behavior. In the case of the dislocation term, the DRX effects were modeled considering the critical strain for DRX initiation and the DRX rate, which are both temperature-and strain rate-dependent. In the Hall-Petch effect term, the dependence of the Hall-Petch coefficient on the processing conditions was considered and the loss of Hall-Petch strengthening with deformation was modeled. Using the proposed model, the work-hardening and flow-softening behavior and microstructure evolution in Ti-6Al-2Zr-1Mo-1V alloys subjected to TMP were predicted. A good agreement could be observed between the experimental and predicted results. This study provides a solution for modeling work-hardening and flow-softening behavior and helps us understand the deformation behavior of two-phase titanium alloys subjected to TMP.

Analytical model of work hardening and simulation of the distribution of hardening in micro-milled nickel-based superalloy

During the process of micro-milling nickel-based superalloy, the cutting surface is strengthened along with the high strain and strain rate, which leads to work hardening and affects the quality of parts and the tool’s life. At present, there are few analytical models that can predict the micro-hardness of the micro-milled surface. Therefore, the authors focus on the research of the micro-milling work hardening of nickel-based superalloy. Firstly, based on the stress-strain relationship and strain-hardening characteristics of Inconel718, the relationship between hardness and strain of Inconel718 is obtained. Then, based on the established micro-milling force model, the stress of a point in the process of micro-milling is derived. Finally, the surface hardness value of the machined surface is predicted by combining the relationship between the stress-strain and the hardness of the workpiece. In addition, a 3D simulation model of micro-milling nickel-based superalloy groove is established by Deform-3D software to research the distribution of micro-hardness of the machined surface. The research offers reference for improving the surface integrity and fatigue performance of micro-milling nickel-based superalloy and explores a feasible way for revealing the mechanism of micro-milling hardening.

A Combined Precipitation, Yield Stress, and Work Hardening Model for Al-Mg-Si Alloys Incorporating the Effects of Strain Rate and Temperature

In this study, a combined precipitation, yield strength, and work hardening model for Al-Mg-Si alloys known as NaMo has been further developed to include the effects of strain rate and temperature on the resulting stress–strain behavior. The extension of the model is based on a comprehensive experimental database, where thermomechanical data for three different Al-Mg-Si alloys are available. In the tests, the temperature was varied between 20 °C and 350 °C with strain rates ranging from 10−6 to 750 s−1 using ordinary tension tests for low strain rates and a split-Hopkinson tension bar system for high strain rates, respectively. This large span in temperatures and strain rates covers a broad range of industrial relevant problems from creep to impact loading. Based on the experimental data, a procedure for calibrating the different physical parameters of the model has been developed, starting with the simplest case of a stable precipitate structure and small plastic strains, from which basic kinetic data for obstacle limited dislocation glide were extracted. For larger strains, when work hardening becomes significant, the dynamic recovery was linked to the Zener-Hollomon parameter, again using a stable precipitate structure as a basis for calibration. Finally, the complex situation of concurrent work hardening and dynamic evolution of the precipitate structure was analyzed using a stepwise numerical solution algorithm where parameters representing the instantaneous state of the structure were used to calculate the corresponding instantaneous yield strength and work hardening rate. The model was demonstrated to exhibit a high degree of predictive power as documented by a good agreement between predictions and measurements, and it is deemed well suited for simulations of thermomechanical processing of Al-Mg-Si alloys where plastic deformation is carried out at various strain rates and temperatures.

Peak Broadening Anisotropy and the Contrast Factor in Metal Alloys

Diffraction peak profile analysis (DPPA) is a valuable method to understand the microstructure and defects present in a crystalline material. Peak broadening anisotropy, where broadening of a diffraction peak doesn’t change smoothly with 2θ or d-spacing, is an important aspect of these methods. There are numerous approaches to take to deal with this anisotropy in metal alloys, which can be used to gain information about the dislocation types present in a sample and the amount of planar faults. However, there are problems in determining which method to use and the potential errors that can result. This is particularly the case for hexagonal close packed (HCP) alloys. There is though a distinct advantage of broadening anisotropy in that it provides a unique and potentially valuable way to develop crystal plasticity and work-hardening models. In this work we use several practical examples of the use of DPPA to highlight the issues of broadening anisotropy.

Modeling of Work Hardening During Hot Rolling of Vanadium and Niobium Microalloyed Steels in the Low Temperature Austenite Region

This work extends the application of the well-established Estrin and Mecking (EM) work-hardening model in unstable low temperature austenite region. The interaction between work hardening, recovery and softening attributed to recrystallization and transformation to ferrite under dynamic conditions is considered. Experimental parameters were varied to study the effects of strain, strain rate and temperature during hot rolling in the low temperature austenite region. Hot compression tests were performed two microalloyed steels—one containing V and the other Nb—at strain rates between 0.1 and 10 s−1 over a temperature range of 750-1000 °C. A model is presented that describes the influence of dynamic recovery on flow behavior in the unstable austenite region. The modified work-hardening model incorporates an additional fitting parameter to the EM model and is dependent on the recovery and softening rates. The new model improved prediction in the unstable austenite region, while the original EM model gave better correlation at relatively higher temperatures when dynamic recrystallization is dominant or at relatively lower temperatures when only dynamic recrystallization to ferrite was the softening mechanism.

Microstructure-dependent mechanical properties of semi-solid copper alloys

Rotary swaging strain induced melt activation (RSSIMA) method is proposed to fabricate semi-solid copper alloys. The micro-grains size evolution of the globular particles during isothermal heat treatments is described by the Lifshize-Slorovitze-Wagner (LSW) equation and mechanical behaviors of semi-solid copper alloys and as-cast copper alloys are analyzed with the power-law Holloman work-hardening model. The effects of microstructure alteration on elasto-plastic properties of semi-solid tin copper alloys are reported. It has been discovered that the stiffness and strength of the alloy samples increase as micro-grain sizes decrease, whereas the alloys originated from various isothermal heat treatments. The strength of the semi-solid samples with globular micro-grains is also discovered to be higher than the strength of as-cast copper with dendrite micro-grains. These enhancements in mechanical properties can be understood by fine-grain mechanisms and precipitation strengthening of the second phase based on microscopy observations. These results can be essential for applications of semi-solid metal alloys.

Investigation of grain subdivision at very low plastic strains in a magnesium alloy

In-situ tensile loading combined with electron backscatter diffraction (EBSD) measurements has been used to investigate the plastic deformation of a magnesium alloy. A novel EBSD mapping is presented, based on construction of maps showing the rotation axis component in the sample coordinate frame of the misorientation from each pixel to the average grain orientation in the deformed sample. Using this mapping it is shown that the pattern of grain subdivision, even at very low plastic strains, can be revealed simultaneously in a large number of grains. In addition, it is demonstrated how maps of the rotation axis corresponding to the misorientation between each pixel and the initial grain orientation provide complimentary information directly useful for crystal plasticity analysis. A detailed slip system analysis shows that the grain subdivision can be accounted for according to the low energy dislocation structures (LEDS) model of work-hardening by differences in the slip amplitudes within different parts of each grain.

Peak stress studies of hot compressed TiHy 600 alloy

TiHy 600 is a near alpha titanium alloy similar to IMI 834 Ti alloy, widely used for gas turbine engine applications such as disc and blades for high pressure compressors. Flow behavior of TiHy 600 alloy is investigated by conducting hot compression tests at temperatures ranging from 900°C to 1050°C with in the strain rate range of (0.001/s) respectively up to 50% deformation. Constitute modeling of work hardening is established, using Cingara equation to verify the stress up to peak stress. It was found that experimental true stress-true strain curves are in good agreement with Cingara equation curves for all temperatures at strain rate of (0.001/s)up to their peak stress values. The average activation energy (Q) is calculated from the peak stress of the flow curves using the hyperbolic-sine law equation (Arrhenius equation) i.e. 851.506KJ/mol. The microstructures of 50% deformed samples are correlated with the post-peak stress flow curve, performed mainly to compare the various softening processes (DRV or DRX).

A microstructure-based yield stress and work-hardening model for textured 6xxx aluminium alloys

The plastic properties of an aluminium alloy are defined by its microstructure. The most important factors are the presence of alloying elements in the form of solid solution and precipitates of various sizes, and the crystallographic texture. A nanoscale model that predicts the work-hardening curves of 6xxx aluminium alloys was proposed by Myhr et al. The model predicts the solid solution concentration and the particle size distributions of different types of metastable precipitates from the chemical composition and thermal history of the alloy. The yield stress and the work hardening of the alloy are then determined from dislocation mechanics. The model was largely used for non-textured materials in previous studies. In this work, a crystal plasticity-based approach is proposed for the work hardening part of the nanoscale model, which allows including the influence of the crystallographic texture. The model is evaluated by comparison with experimental data from uniaxial tensile tests on two textured 6xxx alloys in five temper conditions.

Determination of Soil Parameters to Analyze Mechanical Behavior Using Lade's Double-Surface Work-Hardening Model

In this study, Lade's double-surface work-hardening constitutive model was adopted which uses the elasto-plasticity model as a basic conceptual framework. The model can analyze work hardening and work softening of nonlinear stress-strain behavior, and is regarded as superior to other elasto-plasticity constitutive models in terms of estimation. In the double-surface work-hardening constitutive model, 14 soil parameters are needed to estimate soil behaviors. To determine them, laboratory tests—isotropical consolidation test and conventional compression test—were conducted. Determining of soil parameters is highly complicated and time-consuming; randomness cannot be ruled out in determining parameters that are sensitive to stress-strain estimation, and error may occur. For this reason, a linear and nonlinear regression analysis was used to determine soil parameters. In estimation of undrained behavior, the estimated stress-strain behavior based on the two constitutive models largely overlapped with the test results. However, in estimating drained behavior, the outcome of the two models and the test results were mostly the same, but between the two models, the double-surface work-hardening constitutive model had a sharper slope in initial stress state, and a smaller maximum deviatoric stress.

Identification of material parameters for thin sheets from single biaxial tensile test using a sequential inverse identification strategy

An inverse analysis methodology to simultaneously identify the parameters of various anisotropic yield criteria together with isotropic work-hardening models of metal sheets is outlined. This identification makes use of results of the cruciform biaxial test, i.e., the evolution of the force during the test, for the two axes of the sample, and the major and minor strain distributions along both axes, at a given moment during the test. Based on a study of the sensitivity of the constitutive parameters to the biaxial tensile test results, the inverse identification consists on a procedure that sequentially minimises the gap between experimental and numerical results. Each step of the sequence uses a distinct cost function according to the type of results to be minimised, using a gradient-based optimisation algorithm, the Levenberg-Marquardt method. The inverse methodology allows for the identification of constitutive parameters of complex constitutive models. This sequential identification strategy is compared to a strategy based on a single cost function, involving all parameters and type of results, which has lower performance.

Anisotropic Constitutive Model for Predictive Analysis of Composite Laminates

An anisotropic plastic constitutive model for fiber-reinforced composite material, is developed, which is simple and efficient to be implemented into computer program for a predictive analysis procedure of composite laminates. An anisotropic initial yield criterion, as well as work-hardening model and subsequent yield surface are established that includes the effects of different yield strengths in each material direction, and between tension and compression. The current model is implemented into a computer code, which is Predictive Analysis for Composite Structures (PACS). The accuracy and efficiency of the anisotropic plastic constitutive model and the computer program PACS are verified by solving a number of various fiber-reinforced composite laminates. The comparisons of the numerical results to the experimental and other numerical results available in the literature indicate the validity and efficiency of the developed model. Keywords: Anisotropic Plasticity, Fiber Composite, Predictive Finite Element Analysis

복합재료 거동특성의 파괴해석 I - 이방성 소성 적합모델

A progressive failure analysis procedure for composite laminates is developed in here and in the companion paper. An anisotropic plastic constitutive model for fiber-reinforced composite material, is developed, which is simple and efficient to be implemented into computer program for a predictive analysis procedure of composites. In current development of the constitutive model, an incremental elastic-plastic constitutive model is adopted to represent progressively the nonlinear material behavior of composite materials until a material failure is predicted. An anisotropic initial yield criterion is established that includes the effects of different yield strengths in each material direction, and between tension and compression. Anisotropic work-hardening model and subsequent yield surface are developed to describe material behavior beyond the initial yield under the general loading condition. The current model is implemented into a computer code, which is Predictive Analysis for Composite Structures (PACS), and is presented in the companion paper. The accuracy and efficiency of the anisotropic plastic constitutive model are verified by solving a number of various fiber-reinforced composite laminates with and without geometric discontinuity. The comparisons of the numerical results to the experimental and other numerical results available in the literature indicate the validity and efficiency of the developed model.

복합재료 거동특성의 파괴해석 II - 비선형 유한요소해석

A progressive failure analysis procedure for composite laminates is completed in here. An anisotropic plastic constitutive model for fiber-reinforced composite material is implemented into computer program for a predictive analysis procedure of composite laminates. Also, in order to describe material behavior beyond the initial yield, the anisotropic work-hardening model and subsequent yield surface are implemented into a computer code, which is Predictive Analysis for Composite Structures (PACS). The accuracy and efficiency of the anisotropic plastic constitutive model and the computer program PACS are verified by solving a number of various fiber-reinforced composite laminates with and without geometric discontinuity. The comparisons of the numerical results to the experimental and other numerical results available in the literature indicate the validity and efficiency of the developed model.

Use of Lade's Single Surface Work-Hardening Model to Investigate Mechanical Behavior of Decomposed Soils

In this study, it was attempted to assess soil parameters necessary for Lade's single surface work-hardening model that reviewed the physical and mechanical properties of granite soil located in Korea based on the results of triaxial compression tests. In addition, finite element analyses coupled with the determined soil parameters as inputs were conducted based on Lade's single surface work-hardening model and the results were compared with element test results. It could be seen that, in predicting undrained mechanical behavior, the single surface model was reproducing the stress-strain relation obtained through element tests at high accuracy. It is worthwhile to inform that these differences in the initial loading stage and the impossibility to predict swelling behavior are caused by the fact that there is no prediction model for changes in shear properties, especially in dilatancy properties due to particle crushing occurring while element tests are conducted. Hence, it is concluded that, to expand the applicability of Lade's single surface work-hardening constitutive model to practical problems, the model should be modified in relation to the dilatancy of soils.

Flow stress and work-hardening behaviour of Al–Mg binary alloys

Analysis of the flow stress and work hardening behaviour has been carried out in series of Al–Mg solid solutions between 4K and 298K. The results reveal that the yield stress decreases linearly with the temperature and increases approximately linearly with the Mg content in the solution. The thermomechanical and Portevin–Le Chatelier instabilities dominate the flow stress behaviour of alloys at 4K and 298K. Dynamics of these instabilities increases with the solute content. It is argued that neither PLC nor adiabatic instabilities contribute to the premature failure of the samples. The work-hardening can be reproduced by the Voce type scaling law in a broad range of temperatures. The mean slip distance obtained from the macroscopic model of work hardening is correlated to the scale of the referenced microstructure; Λmin is interpreted as a transition from cell-like to micro shear band microstructure. The failure is discussed in terms of a critical point in a transition form unsaturated to saturated with defects dislocation substructure.

Mechanical Response of Microalloyed Steel Subjected to Nonlinear Deformation

Microalloyed steels have been the subject of theoretical and experimental studies revealing their exceptional mechanical response under nonlinear deformation conditions. In microalloyed steels, especially in multiphase steels, the mechanical properties are adjusted by combination of microstructure components with different levels of theirs mechanical responses, including hardness and ductility. A comprehensive studies have revealed that a transition from the development of usual bulk dislocation microstructures to more architecture ones occurs when the applied strain path allows to cumulate the deformation energy what is also strictly connected with the chemical and structural compositions of analyzed materials. The study presented here aims at understanding the complex strengthening mechanisms as well as microstructure evolution and to provide a link with the mechanical behaviour of investigated steels under nonlinear deformation conditions. The proper choice of the work hardening model for the cyclic plastic deformation is essential for predicting the inhomogeneities occurring during metal forming. Aim of the current work is to discuss the differences between various hardening models with respect to their capabilities in capturing complex deformation models and possibilities of their direct application to finite element modelling of such deformation processes. The results of experimental studies are integrated with computer modelling and dislocation theory to provide insight into the unprecedented combination of properties achieved in certain multiphase steels such as ultra-high flow strengths, good ductility and workability. Finally, based upon results obtained in performed computer simulations, conclusions regarding the possibilities of potential application of the work hardening models in the identification process parameters, trough the inverse analysis, are drawn.

Modelling the Combined Effect of Room Temperature Storage and Cold Deformation on the Age-Hardening Behaviour of Al-Mg-Si Alloys-Part 1

In the present paper, an extended age hardening model for Al-Mg-Si alloys is presented. In this new approach the combined precipitation, yield strength and work hardening model, known as NaMo Version 1, has been further developed to account for the effects of room temperature storage and cold deformation on the resulting age hardening behaviour. Incorporation of these two new stages in NaMo largely increases the versatility of the model by allowing simulations of complex multi-stage industrial processing involving thermomechanical treatment as well. Part 1 of this work deals with the theoretical background and experimental validation of the extended version of NaMo, while Part 2 focuses on the new applications of the model by showing some numerical examples related to production of automotive body panels.