Effect of strain rate and deformation temperature on strain hardening and softening behavior of pure copper

The effects of the deformation temperature and the strain rate on the hot deformation behavior of pure copper were investigated based on compression tests. The expressions of strain hardening rate, dynamic recrystallization critical stress, saturated stress, dynamic recovery volume fraction and dynamic recrystallization volume fraction were determined. According to the processing map, the instability regions occur in regions of 400?450 °C, 0.001?0.05 s?1 and 450?750 °C, 0.05?1 s?1. The deformation mechanism in the stability region is dynamic recrystallization. The flow stress was predicted. The results also show that the true stress–true strain curves predicted by the extracted model are in good agreement with the experimental results.

Strain Softening and Hardening Behavior in AZ61 Magnesium Alloy

The deformation behavior of AZ61 Mg alloy during hot deformation has been investigated in wide temperature and strain rate range by a Gleeble simulator. Specimens are deformed in compression in the temperature range of 523-673 K and at strain rates of 0.001-1 s-1. It is found that the flow curves exhibit a peak and then decrease towards steady-state of classical DRX, which decrease with rising temperature and decreasing strain rate. The deformation behavior of the specimens can be attributed to the occurrence of strain hardening and softening. As stress decreases, the strain hardening rate declines at a fast rate when temperature rises or strain rate decreases. The shapes of θ-σ curves indicate some important features such as subgrain formation, the criticai stress, the peak stress and steady stress. The onset of DRX can be determined by the point of inflection on θ-σ or Inθ-σ curves.

EFFECT OF MICROSTRUCTURE ON THE HARDENING AND SOFTENING BEHAVIORS OF POLYCRYSTALLINE SHAPE MEMORY ALLOYS PART Ⅰ:MICROMECHANICS CONSTITUTIVE MODELING

The effects of microstructure and its evolution on the macroscopic superelastic stress-strain response of polycrystalline Shape Memory Alloy(SMA)are studied by a microstructure-based constitutive model developed in this paper.The model is established on the following basis:(1)the transformation conditions of the unconstrained single crystal SMA microdomain(to be distinguished from the bulk single crystal),which serve as the local criterion for the derivation of overall transfor- mation yield conditions of the polycrystal;(2)the micro-to macro-transition scheme by which the connection between the polycrystal aggregates and the single crystal microdomain is established and the macroscopic transformation conditions of the polycrystal SMA are derived;(3)the quantitative incorporation of three microstruc- ture factors(i.e.,nucleation,growth and orientation distribution of martensite)into the modeling.These microstructural factors are intrinsic of specific polycrystal SMA systems and the role of each factor in the macroscopic constitutive response is quan- titatively modeled.It is demonstrated that the interplay of these factors will result in different macroscopic transformation kinematics and kinetics which are responsible for the observed macroscopic stress-strain hardening or softening response,the latter will lead to the localization and propagation of transformation bands in TiNi SMA.

EFFECT OF MICROSTRUCTURE ON THE HARDENING AND SOFTENING BEHAVIORS OF POLYCRYSTALLINE SHAPE MEMORY ALLOYS PART Ⅱ:NUMERICAL SIMULATION UNDER AXISYMMETRICAL LOADING

Based on the microstructure-based constitutive model established in Part Ⅰ,a detailed numerical investigation on the role of each microstructure pa- rameter in the kinematical and kinetic evolution of polycrystalline SMA under ax- isymmetrical tension loading is performed.Some macroscopic constitutive features of stress-induced martensite transformation are discussed.

Effect of strain hardening and strain softening on welding distortion and residual stress of A7N01-T4 aluminum alloy by simulation analysis

The effect of strain hardening and strain softening behavior of flow stress changing with temperature on welding residual stress, plastic strain and welding distortion of ATN0 1-T4 aluminum alloy was studied by finite simulation method. The simulation results show that the weld seam undergoes strain hardening in the temperature range of 180-250 ℃, however, it exhibits strain softening at temperature above 250 ℃ during welding heating and cooling process. As a result, the strain hardening and strain softening effects counteract each other, introducing slightly influence on the welding residual stress, residual plastic strain and distortion. The welding longitudinal residual stress was determined by ultrasonic stress measurement method for the flat plates of A7N01-T4 aluminum alloy. The simulation results are well accordant with test ones.

A COMBINED PARAMETRIC QUADRATIC PROGRAMMING AND PRECISE INTEGRATION METHOD BASED DYNAMIC ANALYSIS OF ELASTIC-PLASTIC HARDENING/SOFTENING PROBLEMS

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.

Unified simulation of hardening and softening effects for metals up to failure

Toward accurately simulating both hardening and softening effects for metals up to failure,a new finite strain elastoplastic J2-flow model is proposed with the yield strength therein as a function of the plastic work in the explicit form.With no need to identify any adjustable parameters,the uniaxial stress-strain response predicted from this new model is shown to automatically and accurately match any given data from monotonic uniaxial extension tests of bars.As such,the objectives in three respects are achieved for the first time,i.e.,(i)both the hardening and softening effects up to failure can be simulated in the sense of matching test data with no errors,(ii)the usual tedious implicit procedures toward identifying numerous unknown parameters need not be involved and can be totally bypassed,and(iii)the model applicability can be ensured in a broad sense for various metallic materials with markedly different transition effects from hardening to softening.With the new model,the complete response features of stretched bars and twisted tubes up to failure are studied,including the failure effects of bars under monotonic extension and tubes under monotonic torsion and,furthermore,the fatigue failure effects of bars under cyclic loading.The results show accurate agreement with the uniaxial data,and the results for both the shear stress and the normal stress at the finite torsion display realistic hardening-to-softening transition effects for the first time.

Stacking fault energy and electronic structure of molybdenum under solid solution softening/hardening

Ab initio calculations are used to understand the fundamental mechanism of the solid solution softening/hardening of the Mo-binary system.The results reveal that the Mo-Ti,Mo-Ta,Mo-Nb,and Mo-W interactions are primarily attractive with negative heats of formation,while the interactions of Mo-Re,and Mo-Zr would be mainly repulsive with positive heats of formation.It is also shown that the addition of Re and Zr would cause the solid solution softening of Mo by the decrease of the unstable stacking fault energy and the increase of ductility.On the contrary,the elements of W,Ta,Ti,and Nb could bring about the solid-solution hardening of Mo through the impediment of the slip of the dislocation and the decrease of ductility.Electronic structures indicate that the weaker/stronger chemical bonding due to the alloying elements should fundamentally induce the solid solution softening/hardening of Mo.The results are discussed and compared with available evidence in literatures,which could deepen the fundamental understanding of the solid solution softening/hardening of the binary metallic system.

Finite deformation analysis of crack tip fields in plastically compressible hardening–softening–hardening solids

Crack tip fields are calculated under plane strain small scale yielding conditions. The material is characterized by a finite strain elastic-viscoplastic constitutive relation with various hardening-softening-hardening hardness functions. Both plastically compressible and plastically incompressible solids are considered. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The initial crack is taken to be a semi-circular notch and symmetry about the crack plane is imposed. Plastic compressibility is found to give an increased crack opening displacement for a given value of the applied loading. The plastic zone size and shape are found to depend on the plastic compressibility, but not much on whether material softening occurs near the crack tip. On the other hand, the near crack tip stress and deformation fields depend sensitively on whether or not material softening occurs. The combination of plastic compressibility and softening (or softening-hardening) has a particularly strong effect on the near crack tip stress and deformation fields.

APPROXIMATE ESTIMATION OF HARDENING-SOFTENING BEHAVIOUR OF CIRCULAR PIPES SUBJECTED TO PURE BENDING

An approximate method for describing the plastic hardening-softening behaviour of circular pipes subjected to pure bending is presented. Theoretical estimation based on the uniform ovalization model and local collapse model proposed in the paper is incorporated to give several simple formulations with reasonable accuracy for determining the relationship between bending moment (M) and curvature (kappa) in the purely bended pipes. Attention is focused on the critical curvature associated with maximum resistant moment and the maximum change in the original diameter before the end of uniform ovalization stage as well as the local collapse behaviour. Some comparisons between analytical results and experimental results are made in order to examine the theory.

Mesoscopic analysis of the utilization of hardening model for a description of softening behavior based on disturbed state concept theory

Mesoscopic characteristics of a clayey soil specimen subjected to macroscopic loading are examined using a medi- cal-use computerized tomography (CT) instrument. Disturbed state concept (DSC) theory is based on the utilization of the hard- ening model. DSC indirectly describes material behavior by claiming that the actual response of the material is expressed in terms of the relative intact (RI) response and the fully adjusted (FA) response. The occurrence of mesoscopic structural changes of material has similarities with the occurrence of a macroscopic response of the material under loadings. In general, the relative changing value of a softening material is three to five times more than that of a hardening material. Whether special zones exist or not in a specimen cross section does not affect the following conclusion: hardening material and softening material show me- chanical differences with CT statistical indices values prominently changing, and the change is related to the superposing of a disturbance factor. A new disturbance factor evolution function is proposed. Thus, mesoscopic statistical indices are introduced to describe macroscopic behavior through the new evolution function. An application of the new evolution function proves the effectiveness of the amalgamation of a macroscopic and a mesoscopic experimental phenomenon measurement methods.

A work-hardening and softening constitutive model for sand:modified plastic strain energy approach

The paper describes an energy-based constitutive model for sand, which is modified based on the modified plastic strain energy approach, represented by a unique relationship between the modified plastic strain energy and a stress parameter, independent of stress history. The modified plastic strain energy approach was developed based on results from a series of drained plastic strain compression tests along various stress paths on saturated dense Toyoura sand with accurate stress and strain measurements. The proposed model is coupled with an isotropically work-hardening and softening, non-associtated, elasto-plastic material description. The constitutive model concerns the inherent and stress system-induced cross-anisotropic elastic deformation properties of sand. It is capable of simulating the deformation characteristics of stress history and stress path, the effects of pressure level, anisotropic strength and void ratio, and the strain localization.

DAMAGE MODEL FOR HARDENING AND SOFTENING MATERIAL IN GENERAL STATE OF STRESS

The present paper is aimed to simulate progression of damage,hardening and softening response in brittle materials such as concrete or rock in general state of stress.Similar shape of surfaces for yield,failure and damage progressing are available,and softening strain is treated as plasticity.Then,the proposed model is applied to solving several boundary value problems.

A refined deviatoric hardening plastic model for sand

The classical deviatoric hardening models are capable of characterizing the mechanical response of granular materials for a broad range of degrees of compaction.This work finds that it has limitations in accurately predicting the volumetric deformation characteristics under a wide range of confining/consolidation pressures.The issue stems from the pressure independent hardening law in the classical deviatoric hardening model.To overcome this problem,we propose a refined deviatoric hardening model in which a pressure-dependent hardening law is developed based on experimental observations.Comparisons between numerical results and laboratory triaxial tests indicate that the improved model succeeds in capturing the volumetric deformation behavior under various confining/consolidation pressure conditions for both dense and loose sands.Furthermore,to examine the importance of the improved deviatoric hardening model,it is combined with the bounding surface plasticity theory to investigate the mechanical response of loose sand under complex cyclic loadings and different initial consolidation pressures.It is proved that the proposed pressure-dependent deviatoric hardening law is capable of predicting the volumetric deformation characteristics to a satisfactory degree and plays an important role in the simulation of complex deformations for granular geomaterials.

A vector sum analysis method for stability evolution of expansive soil slope considering shear zone damage softening

Slope stability analysis is a classical mechanical problem in geotechnical engineering and engineering geology.It is of great significance to study the stability evolution of expansive soil slopes for engineering construction in expansive soil areas.Most of the existing studies evaluate the slope stability by analyzing the limit equilibrium state of the slope,and the analysis method for the stability evolution considering the damage softening of the shear zone is lacking.In this study,the large deformation shear mechanical behavior of expansive soil was investigated by ring shear test.The damage softening characteristic of expansive soil in the shear zone was analyzed,and a shear damage model reflecting the damage softening behavior of expansive soil was derived based on the damage theory.Finally,by skillfully combining the vector sum method and the shear damage model,an analysis method for the stability evolution of the expansive soil slope considering the shear zone damage softening was proposed.The results show that the shear zone subjected to large displacement shear deformation exhibits an obvious damage softening phenomenon.The damage variable equation based on the logistic function can be well used to describe the shear damage characteristics of expansive soil,and the proposed shear damage model is in good agreement with the ring shear test results.The vector sum method considering the damage softening behavior of the shear zone can be well applied to analyze the stability evolution characteristics of the expansive soil slope.The stability factor of the expansive soil slope decreases with the increase of shear displacement,showing an obvious progressive failure behavior.

Alternative splicing of the PECTINESTERASE gene encoding a cell wall-degrading enzyme affects postharvest softening in grape

The firmness of table grape berries is a crucial quality parameter. Despite extensive research on postharvest fruit softening, its precise molecular mechanisms remain elusive. To enhance our comprehension of the underlying molecular factors, we initially identified differentially expressed genes(DEGs) by comparing the transcriptomes of folic acid(FA)-treated and water-treated(CK) berries at different time points. We then analyzed the sequences to detect alternatively spliced(AS) genes associated with postharvest softening. A total of 2,559 DEGs were identified and categorized into four subclusters based on their expression patterns, with subcluster-4 genes exhibiting higher expression in the CK group compared with the FA treatment group. There were 1,045 AS-associated genes specific to FA-treated berries and 1,042 in the CK-treated berries, respectively. Gene Ontology(GO) annotation indicated that the AS-associated genes in CK-treated berries were predominantly enriched in cell wall metabolic processes,particularly cell wall degradation processes. Through a comparison between treatment-associated AS genes and subcluster-4 DEGs, we identified eight genes, including Pectinesterase 2(VvPE2, Vitvi15g00704), which encodes a cell wall-degrading enzyme and was predicted to undergo an A3SS event. The reverse transcription polymerase chain reaction further confirmed the presence of a truncated transcript variant of VvPE2 in the FA-treated berries.Our study provides a comprehensive analysis of AS events in postharvest grape berries using transcriptome sequencing and underscores the pivotal role of VvPE2 during the postharvest storage of grape berries.

Influence of thermomechanical treatment on recrystallization and softening resistance of Cu-6.5Fe-0.3Mg alloy

The recrystallization and softening resistance of a Cu-6.5Fe-0.3Mg(mass fraction,%)alloy prepared by Process 1(cold rolling heat treatment)and Process 2(hot/cold rolling heat treatment)were studied using Vickers hardness tests,tensile tests,scanning electron microscopy and transmission electron microscopy.The softening temperature,hardness and tensile strength of the alloy prepared by Process 2 were 110°C,HV 15 and 114 MPa higher,respectively,than those of the alloy prepared by Process 1 after aging at 300°C.The recrystallization activation energy of the alloys prepared by Process 1 and Process 2 were 72.83 and 98.11 kJ/mol,respectively.The pinning effects of the precipitates of the two alloys on grain boundaries and dislocations were basically the same.The softening mechanism was mainly attributed to the loss of dislocation strengthening.The higher Fe fiber density inhibited the average free migration path of dislocations and grain boundary migration in the alloy,which was the main reason for higher softening temperature of the alloy prepared by Process 2.

Experimental Procedure and Hardening Model to Consider Forming and Baking Effects in Simulation

This paper investigated an experimental method for bake hardening properties, a technique for deriving the true stress-strain curves after reaching the maximum load, and a constitutive equation considering both work hardening and bake hardening in order to apply the work hardening occurring in the forming process of parts and the bake hardening induced in the baking process to an automotive crash simulation. A general bake hardening test is that a pre-tensioned specimen is baked and then the same specimen is tensioned again without any further treatment. For a bake hardening test of automotive steel with a tensile strength of 1.2 GPa or more, fractures often occur in curvature section outside, an extensometer due to the difference in the material strength caused by non-uniform bake hardening. This causes a problem in that the bake hardening properties cannot be obtained. In this paper, to prevent curvature fracture, tensile specimens were re-machined in the uniformly deformed region of large specimens subjected to pre-strain, and the re-machined specimens with uniform strength in all regions were re-tensioned. In the bake hardening test of ultra-high strength steels with a tensile strength of 1 GPa or more, shear band fractures occur when the pre-strain is large. This makes it impossible to obtain a true stress-strain curve because there is no uniformly deformed region under a tensile test. To overcome this problem, a new method to calculate the true stress-strain curve by comparing experimental results and the load calculated by the local strain obtained from digital images was developed. This method can be applied not only where shear band deformation occurs, but also in necking deformation, and true stress-strain curves for strains up to 2 - 3 times the uniform elongation can be obtained. A new constitutive equation was developed since an appropriate hardening model is required to simultaneously apply the work hardening and the bake hardening to the simulation. For the newly developed model, the user material subroutine of LS-Dyna was configured, and the simulation was performed on the single hat specimens with pre-strain. When both work hardening and bake hardening were considered, there was a significant increase in absorbed energy compared to when only work hardening was considered. This means that both work hardening and bake hardening should be considered in the car crash simulations to enhance the accuracy of the simulation.

Flow softening behavior and microstructure evolution of Al-5Zn-2Mg aluminum alloy during dynamic recovery

The flow stress behavior and microstructure development of Al-5Zn-2Mg （7005） aluminum alloy were studied by hot compression tests at deformation temperatures between 300-500 ＆#176;C and strain rates between 0.05-50 s-1. The deformed structures of the samples were observed by optical microscopy （OM）, transmission electron microscopy （TEM） and electron backscattering diffraction （EBSD） analysis. The calculated activation energy is 147 kJ/mol, which is very close to the activation energy for lattice self-diffusion in aluminum （142 kJ/mol）. Dynamic recovery is the dominant restoration mechanism during the deformation. At high strain rate of 50 s-1, temperature rise due to deformation heating leads to a significant flow softening. Microstructure observations indicated that the remaining softening after deformation heating correction at high strain rate and the softening observed at high temperature are associated with grain coarsening induced by grain boundary migration during dynamic recovery process.

Modeling of strain hardening and dynamic recrystallization of ZK60 magnesium alloy during hot deformation

The flow stress behavior of ZK60 alloy at elevated temperature was investigated. The strain hardening and dynamic recrystallization of the alloy were modeled by Kocks-Meching model and Avrami equation, respectively. A new constitutive equation during hot deformation was constructed to predict the flow stress considering the dynamic recrystallization. The results show that the flow stress curves predicted by the proposed equation have high correlation coefficients with the experimental data, which confirms that the developed model is accurate and effective to establish the flow stress equation of ZK60 magnesium alloy during hot deformation. Microstructure observation shows that dynamic recovery occurs in the initial stage of hot deformation. However, the microstructure turns to recrvstallization structure as the strain increases.