Determination of critical strain for initiation of dynamic recrystallization

Using the work hardening rate–strain curves, an effective mathematical model has been developed to predict the stress–strain curves of alloy steel during hot deformation up to the peak stress regardless of the level of the strain, weather smaller or larger than the critical strain. This model is expressed in terms of peak stress, peak strain and one temperature-sensitive parameter, S. In addition, one new model, which is a function of peak strain, was proposed to predict the critical strain for the initiation of dynamic recrystallization using the second derivative of work hardening rate with respect to stress. Besides the theoretical study, the analysis is used to determine the stress–strain curves and critical strain of 304 austenitic stainless steel. The predicted results were found to be in accord with the experimental data.     

Research on the dynamic recrystallization behavior of GCr15 steel

The dynamical recrystallization (DRX) of GCr15 steel was investigated at deformation temperatures of 950–1150 °C and strain rates of 0.1–10 s^?1 on a Gleeble-3800 thermo-mechanical simulator. The stress–strain curves at lower strain rates are typical of the occurrence of DRX and exhibit a peak in the flow stress before reaching steady state. The flow stress at higher strain rates increases rapidly to the maximum too, but followed by a steady region. The microstructures after deformation certify that DRX takes place in all specimens. And the results show that DRX occurs more easily with the decrease of strain rate and the increase of deformation temperature. Using regression analysis, the DRX activation energy of the steel, the relationship of critical strain and deformation conditions were determined. In order to determine the recrystallized fraction under different conditions, an approximate model based on the stress–strain curves was investigated, and the kinetic model for DRX was established.     

Overall stress–strain relationship of cold rolled transformation induced plasticity multiphase steels

Abstract

As a result of transformation induced plasticity, TRIP assisted steels possess favourable mechanical properties such as high strength, ductility and toughness. In the present work, the flow stress of a cold rolled TRIP multiphase steel has been calculated from the stress of individual constituent phases on the basis of a continuum model whereby the internal stress produced by the inhomogeneous distribution of plastic strain is considered. For the first time, account is taken of how the volume fraction of constituent phases changes with strain. A comparison of stress–strain curves determined from the model and experimentally derived stress–strain curves for an Si–Mn type TRIP800 steel gives satisfactory agreement. Variation of the strain hardening exponent of the TRIP steel with strain is also discussed.     

Characterization and modeling of stain-rate-dependent behavior of polymeric foams

A polymeric foam was characterized under quasi-static and dynamic loading and a constitutive model was proposed to describe its nonlinear behavior at varying strain rates. Four characteristic properties were identified in the compressive stress–strain curves: (1) yield stress, (2) peak or “critical” stress corresponding to collapse initiation of the cells, (3) plateau stress following the initial collapse of the cells, and (4) strain hardening stress at the end of the plateau region and before the onset of densification. All of the above characteristic stresses vary linearly with the logarithm of strain rate. A strain-based nonlinear constitutive model was proposed. A unified (master) constitutive model with built-in strain rate dependence was formulated and was shown to be in very good agreement with experimental results. The master stress–strain response was modeled in two parts, a power law and one consisting of two exponential terms.     

Determination of Critical Conditions for Initiation of Dynamic Recrystallization by New Method

Based on the stress versus strain relation for materials at high temperatures, a new method to determine critical conditions for initial dynamic recrystallization (DRX) was proposed by analyzing the stress versus strain curve in a double natural logarithm coordinates (Ln–Ln plot) directly. The critical conditions of initial DRX of a low carbon steel were determined by the new method and the resultant values were compared with those determined by previous methods. The results show that the normalized strains are 0.6491, 0.7026, and 0.7055, respectively, by using the corresponding curves and all of the values fall in the range of 0.6–0.85 proposed by Sellars. The normalized stress and strain determined by using the strain hardening rate versus stress curve have a good agreement with those determined by using the stress versus strain curve in an Ln–Ln plot.     

钒氮微合金钢动态再结晶动力学及影响因素

为研究钒氮微合金钢的动态再结晶动力学及影响因素,选取3种对比成分的钒氮微合金钢发生动态再结晶的流变应力曲线,利用硬化速率一应力(θ-σ)曲线获得了饱和流变应力σsat、峰值应力σp、动态再结晶临界应力σc及稳态应力σss的准确值及上述特征应力值与σp的依赖关系,回归得到应变速率敏感的中碳钒氮微合金钢动态再结晶临界应变ε...     

A Semiempirical Model for Post-Yield Stress Instability in the Stress–Strain Response of 3D Lattice Structures under Compressive Loads

Mechanical behavior of lattice structures is important for a range of engineering applications. Herein, a new semiempirical model is proposed that describes the entire range of stress–strain response of lattice structures, including the stress-instability region which is modeled as an oscillator. The model can be fit to individual stress–strain curves to extract elastic modulus, yield stress, collapse stress, post-yield collapse ratio, densification strain, and the energy absorbed per unit volume. The model is fit to 119 unique experimental stress–strain curves from 13 research papers in literature covering four different lattice designs, namely, octet truss, body-centered cubic with vertical members, body-centered cubic, and hexagonal. Manufacturing methods (additive and conventional) and materials (metals and polymers) were also included in the analysis. The fitted model yields several new insights into the compression behavior of previously tested lattice structures and can be applied to additional lattice designs. Among other results, analysis of variance (ANOVA) reveals that the octet truss lattice demonstrates the highest post-yield collapse ratio and the smallest normalized energy absorption per unit volume amongst the lattice structures investigated. The proposed model is a powerful tool for designers to quantitatively compare and select 3D lattice structures with the desired mechanical characteristics.     

Ti-6Al-2Zr-1Mo-1V合金热变形激活动态再结晶的临界条件识别及表征

热压缩实验获得Ti-6Al-2Zr-1Mo-1V合金在温度1073～1323K,应变速率0.01～10s-1条件下的真应力-应变曲线,以此作为识别及表征动态再结晶临界条件的底层数据。对比分析流变应力曲线发现高温、低应变速率下动态回复型软化态势显著;低温、高应变速率下动态再结晶型软化态势显著。引入材料加工硬化率θ,结合θ-σ曲线拐点判据识别了流变应力曲线隐含表征激活动态再结晶的特征参量:临界应变、临界应力。采用含动态再结晶激活能Q的Arrhenius方程求得α、β、n1、n2等材料常数并获得该合金动态再结晶激活能对应变速率及温度的响应图。进一步引入表征动态再结晶临界条件的临界应变模型,获得了临界应变与各热力参数之间的数学关系,验证表明该临界模型预测精度最大为12.9%。     

Application of optical field analysis of tensile tests for calibration of the Rusinek–Klepaczko constitutive relation of Ti6Al4V titanium alloy

In this paper, the application of the Rusinek–Klepaczko relation to describe the constitutive behaviour of Ti6Al4V titanium alloy with an HCP crystalline structure was proposed. The calibration of model coefficients was carried out on the basis of tensile tests. To obtain true stress–strain curves at quasi-static and dynamic loading conditions, the optical field measurement method was applied to determine the history of specimen cross-sections at the necking point. The outline of the specimen was tracked by virtual strain gauges implemented in TEMA Motion software. Adiabatic characteristics obtained at high strain rates using a pre-tension Hopkinson bar were corrected into quasi-isothermal using an analytical approach. Subsequently, a visco-plastic model calibrated using introduced methodology was validated using the finite element method. Engineering stress–strain curves, calculated using ABAQUS software incorporating the Rusinek–Klepaczko model, showed good agreement with experimental data at both quasi-static and dynamic deformation regimes. Moreover, numerical analysis of tensile tests shows that the strain, temperature and stress triaxiality distribution is non-homogenous in specimen cross-sections perpendicular to the loading direction. The value of the strain, temperature and stress triaxiality also depends on the strain rate.     

Modelling of flow stress of dual phase steel under warm tensile deformation

Abstract

In order to evaluate the flow stress of dual phase high strength steel in warm forming processes, the flow stress behaviours of dual phase steel were investigated at different temperatures and strain rates. A mathematical model is proposed to predict the stress–strain curves of dual phase steel during warm tension by employing the hyperbolic sine function of Zener–Hollomon parameter, which can describe the relationship among temperature, strain rate and flow stress under warm tensile deformation correctly. Material constants in the equation are expressed in polynomial form of strain. Parameters in the polynomials were obtained by least square method. The predicted stress–strain curves are in good agreement with experimental results, which confirms that the proposed model is accurate.     

A modified Johnson–Cook constitutive model for Mg–Gd–Y alloy extended to a wide range of temperatures

In this paper, a new phenomenological and empirically based constitutive model was proposed to change the temperature term in the original Johnson–Cook constitutive model. The new model can be used to describe or predict the stress–strain relation of the metals deformed over a wide range of temperatures even though the current temperatures were lower than the reference temperature. Based on the impact compression data obtained by split Hopkins pressure bar technique, the material constants in the new model can be experimentally determined using isothermal and adiabatic stress–strain curves at different strain rates and temperatures. Good agreement is obtained between the predicted and the experimental stress–strain curves for a hot-extruded Mg–10Gd–2Y–0.5Zr alloy at both quasi-static and dynamic loadings under a wide range of temperatures ever though the current temperatures were lower than the reference temperature.     

Assessment and modelling of isothermal forging of intermetallic compounds Part 1 – TiAl

Abstract

In this, the first of four papers concerned with the isothermal forging of intermetallic compounds, Ti–48Al–2Mn–2Nb (at.-%), an alloy based on the γ-TiAl intermetallic phase, has been deformed over the temperature and strain rate ranges 1050–1125°C and 3·0 × 10^-4–3·0 × 10^-2 s^-1 respectively. Examination of the stress–strain curves shows an increase in flow softening behaviour with increasing temperature and decreasing strain rate, contrary to what might have been expected. Forged microstructures indicate that grain refinement via dynamic recrystallisation has occurred, resulting in a fine, almost fully γ microstructure. Constitutive data calculated from initial stress–strain curves (for example activation energy of deformation and strain rate sensitivity) have been used to model deformation behaviour with a reasonable degree of success.     

Single-Stage Models of Stress–Strain Curves Up to Maximum Load: Duplex Stainless Steel and High-Strength Steels

There is a need for developing an accurate and united mathematical model representing tensile engineering stress–strain curves of duplex stainless steels and high-strength steels up to maximum load.     

Hot deformation behaviour and constitutive modelling of P92 heat resistant steel

Abstract

Hot compression tests are conducted in the present paper to investigate hot deformation behaviour of the newly developed heat resistant steel P92, which is used to fabricate main steam pipes for ultra supercritical power plants. Stress–strain curves at elevated temperatures and different strain rates are obtained. It is found that dynamic recrystallisation happens only when the temperature is above 1100°C and strain rate is below 0·1 s^?1. Otherwise, dynamic recovery is the main softening mechanism. Constitutive modelling with the hyperbolic sine, including an Arrhenius term, is used to predict peak and saturated stresses. Material constants for this model are determined. Results show that the model can be used to predict peak and saturated stresses. However, the model would fail in predicting flow stress with respect to strain; thus, a model containing nine independent parameters and the complete form of Spittel equation are utilised to predict flow stress curves softened by dynamic recrystallisation and dynamic recovery respectively since there are no unified equations. The predicted stress–strain curves are in good agreement with experimental results, which confirmed that the models developed in the present paper are effective and accurate for P92 steel.     

Basis for viscoelastic modelling of polyethylene terephthalate (PET) near Tg with parameter identification from multi-axial elongation experiments

The mechanical response of Polyethylene Terephthalate (PET) in elongation is strongly dependent on temperature, strain and strain rate. Near the glass transition temperature T_g, the stress vs strain curves present a strain hardening effect vs strain under conditions of large deformations. At a given strain value, the strain rate has also an increasing influence on the stress value. The main goal of this work is to propose a visco-elastic model to predict the PET behaviour when subjected to large deformations and to determine the material properties from the experimental data. The visco-elastic model is written in a Leonov like way and the variational formulation is carried out for the numerical simulation using this model. To represent the non–linear effects, an elastic part depending on the elastic equivalent strain and a non-Newtonian viscous part depending on both viscous equivalent strain rate and cumulated viscous strain are tested. The model parameters can then be accurately obtained through the comparison with the experimental uniaxial and biaxial tests.     

Disorder is good for you: the influence of local disorder on strain localization and ductility of strain softening materials

We formulate a generic concept model for the deformation of a locally disordered, macroscopically homogeneous material which undergoes irreversible strain softening during plastic deformation. We investigate the influence of the degree of microstructural heterogeneity and disorder on strain localization (formation of a macroscopic shear band) in such materials. It is shown that increased microstructural heterogeneity delays strain localization and leads to an increase of the plastic regime in the macroscopic stress–strain curves. The evolving strain localization patterns are characterized.     

An estimation of true Ramberg‐Osgood curve parameters for materials with and without Luder's strain using yield and ultimate strengths

Engineering tensile stress–strain curves for metallic materials typically show two different behaviours, namely, with Luder's strain and without Luder's strain. Luder's strain is more common for ductile materials, whereas high‐strength steels deform without Luder's strain. Usually, the stress–strain curves of ductile steels exhibit ultimate load where necking starts to develop. On the other hand, steels with low ductility exhibit monotonic increase of the applied load till failure without necking. Recently, Kamaya proposed a method to estimate the Ramberg‐Osgood relationship parameters for true stress–strain curves on the basis of conventional yield and ultimate strengths. This method can be not accurate enough for ductile materials exhibiting Luder's strain. Hence, a more general procedure for the materials exhibiting Luder's strain is proposed. In addition, an inverse method for assessing an ‘apparent ultimate tensile stress’ (akin to the ultimate stress of ductile materials at point of zero slope) for materials with low ductility (due to quenching or carburizing) is suggested.     

Dynamic Recrystallization Behavior of 13%Cr Martensitic Stainless Steel under Hot Working Condition

In this study,the effect of hot deformation on martensitic stainless steel was carried out in temperatures between 950 to 1100℃and strain rates of 0.001,0.01 and 0.1 s-1.Two important dynamic recrystallization parameters,the critical strain and the point of maximum dynamic softening,were derived from strain hardening rate vs stress curves.Then the calculated parameters were used to predict the dynamic recrystallized fraction.Our results show that critical stress and strain increase with decreasing deformation temperature and increasing strain rate.The hot deformation activation energy of the steel is also investigated in the present work with 413 kJ/mol.Our experimental flow curves are in fair agreement with the kinetics of dynamic recrystallization model.