Prediction of non-proportional cyclic hardening and multiaxial fatigue life for FCC and BCC metals under constant amplitude of strain cycling

The fatigue lives are reduced accompanying an additional cyclic hardening under strain controlled non-proportional cyclic loading in which principal directions of stress and strain are altered within a cycle. This study predicts non-proportional cyclic hardening and multiaxial fatigue life for several BCC and FCC metals under constant amplitude strain cycling. A novel procedure to determine non-proportional cyclic hardening form uniaxial tensile properties has discussed in this study. Standard plastic strain energy density based fatigue criteria with considering the non-proportional cyclic hardening effect successfully predicts multiaxial fatigue lives. The predictions of non-proportional cyclic hardening and multiaxial fatigue life through models are validated by experimental results of various BCC and FCC metals which are collected from literatures.

Constitutive modelling of drawing and extrusion with cyclic torsion

In the current work, constitutive models are developed to describe the cyclic hardening and softening led by the strain path chaneg.  The contribution of deformation conditions such as drawing and extrusion speed, cyclic rotating angle on the drawing and extrusion force will be investigated.  The development of such constitutive models will provide insight into the optimization of operation conditions to explore the potential of industrial applications.

Analysis of work hardening and recrystallization during the hot working of steel using a statistically based internal variable model

A mathematical model has been developed which describes the hot deformation and recrystallization behavior of austenite using a single internal variable: dislocation density. The dislocation density is incorporated into equations describing the rate of recovery and recrystallization. In each case no distinction is made between static and dynamic events, and the model is able to simulate multideformation processes. The model is statistically based and tracks individual populations of the dislocation density during the work-hardening and softening phases. After tuning using available data the model gave an accurate prediction of the stress–strain behavior and the static recrystallization kinetics for C–Mn steels. The model correctly predicted the sensitivity of the post deformation recrystallization behavior to process variables such as strain, strain rate and temperature, even though data for this were not explicitly incorporated in the tuning data set. In particular, the post dynamic recrystallization (generally termed metadynamic recrystallization) was shown to be largely independent of strain and temperature, but a strong function of strain rate, as observed in published experimental work.

Effect of martensite volume fraction on low cycle fatigue behaviour of dual phase steels: experimental and microstructural investigation

The low cycle fatigue (LCF) behaviour of a dual phase (DP) steel with different martensite volume fractions has been investigated, with particular focus on fatigue life, cyclic hardening/softening behaviour and microstructural evolution. DP steels with martensite volume fractions between 13% and 88% were produced and their monotonic and cyclic deformation behaviours evaluated. The LCF life has been examined in depth and compared with published literature. It has been concluded that, once normalised for plastic strain amplitude, the fatigue life was found to be significantly reduced by an increase in the martensite volume fraction. All alloys were observed to show some initial cyclic hardening followed by cyclic softening. Clear sub-cell formation occurred in ferrite grains irrespective of the martensite volume fraction, and it is suggested that this cell formation and martensite softening are responsible for the cyclic softening behaviour.

Effect of martensite morphology on low cycle fatigue behaviour of dual phase steels: Experimental and microstructural investigation

The low cycle fatigue (LCF) behaviour of a dual phase (DP) steel with different martensite morphologies has been investigated in the present work. DP steels with coarse martensite morphologies show inferior LCF life in comparison with fine martensite morphologies for all martensite volume fractions examined. It is suggested that this is be due to the development of larger local plastic strain concentrations in the ferrite with a coarser microstructure, compared to the finer microstructural morphology. Fatigue cracks were observed to initiate inside ferrite grains, and to preferentially propagate through the softer ferrite phase. The average sub-cell size was finer in samples with higher martensite volume fractions, but the sub-cell size was almost unaffected by the martensite morphology.

Material properties under drawing and extrusion with cyclic torsion

A copper bar was drawn while a lead bar was extruded through a cyclically twisting die in a specifically designed experimental rig. The drawing/extrusion load fluctuated at the same frequency as that of die twisting. The load tended to be at a level of monotonic deformation when the die was changing direction. The degree of the reduction in load for both the drawing and extrusion processes depended on the deformation conditions and requires optimisation for industrial application.

Microstructure evolution and softening processes occurring during annealing of hot deformed Ni-30Fe austenite

The current work investigates the microstructure evolution and softening processes that take place during annealing of an austenitic Ni-30Fe model alloy subjected to hot deformation in the dynamic recrystallization (DRX) regime. The substructure of the deformed matrix grains largely comprised organized microband arrays, though that of the DRX grains consisted of more random, complex subgrain/cell arrangements. This substructure disparity was also reflected by the distinct difference in the mechanism of post-deformation softening taking place during annealing of the deformed matrix and DRX grains. In the former, the recrystallization process took place through nucleation and growth of new grains fully replacing the deformed structure, as expected for the classical static recrystallization (SRX). The corresponding texture was essentially random, in contrast to that of the DRX grains dominated by low Taylor factor components. The microbands originally present within the deformed matrix grains displayed some tendency to disintegrate during annealing, nonetheless, they remained largely preserved even at prolonged holding times. During annealing of the fully DRX microstructure, a novel softening mechanism was revealed. The initial post-dynamic softening stage involved rapid growth of the dynamically formed nuclei and migration of the mobile boundaries in correspondence with the well-established metadynamic recrystallization (MDRX) mechanism. However, in contrast to the deformed matrix, SRX was not observed and the sub-boundaries within DRX grains rapidly disintegrated through dislocation climb and dislocation annihilation, which led to the formation of dislocation-free grains already at short holding times. Consequently, the DRX texture initially became slightly weakened and then remained largely preserved throughout the annealing process.

Texture evolution and softening processes in an austenitic Ni-30Fe alloy subjected to hot deformation and subsequent annealing

The current work has investigated the texture development in an austenitic Ni-30Fe model alloy during deformation within the dynamic recrystallization (DRX) regime and after post-deformation annealing. Both the deformed matrix and DRX texture displayed the expected FCC shear components, the latter being dominated by the low Taylor factor grains, which was presumably caused by their lower consumption rate during DRX. The deformed matrix grains were largely characterized by organized, microband structures, while the DRX grains showed more random, complex subgrains/cell arrangements. The latter substructure type proved to be significantly less stable during post-deformation annealing. The recrystallization of the deformed matrix occurred through nucleation and growth of new grains fully replacing the deformed structure, as expected for the classical static recrystallization (SRX). Unlike the DRX grains, the SRX texture was essentially random. By contrast, a novel softening mechanism was revealed during annealing of the fully DRX microstructure. The initial post-dynamic softening stage involved rapid growth of the dynamically formed nuclei and migration of the mobile boundaries in line with the well-established metadynamic recrystallization (MDRX) mechanism, which weakened the starting DRX texture. However, in parallel, the sub-boundaries within the deformed DRX grains progressively disintegrated through dislocation climb and dislocation annihilation, which ultimately led to the formation of dislocation-free grains. Consequently, the weakened DRX texture largely remained preserved throughout the annealing process.

Microstructure evolution and softening processes in hot deformed austenitic and duplex stainless steels

The microstructure evolution and softening processes occurring in 22Cr-19Ni-3Mo austenitic and 21Cr-10Ni-3Mo duplex stainless steels deformed in torsion at 900 and 1200 °C were studied in the present work. Austenite was observed to soften in both steels via dynamic recovery (DRV) and dynamic recrystallisation (DRX) for the low and high deformation temperatures, respectively. At 900 °C, an "organised", self-screening austenite deformation substructure largely comprising microbands, locally accompanied by micro-shear bands, was formed. By contrast, a "random", accommodating austenite deformation substructure composed of equiaxed subgrains formed at 1200 °C. In the single-phase steel, DRX of austenite largely occurred through straininduced grain boundary migration accompanied by (multiple) twinning. In the duplex steel, this softening mechanism was complemented by the formation of DRX grains through subgrain growth in the austenite/ferrite interface regions and by large-scale subgrain coalescence. At 900 °C, the duplex steel displayed limited stress-assisted phase transformations between austenite and ferrite, characterised by the dissolution of the primary austenite, formation of Widmanstätten secondary austenite and gradual globularisation of the transformed regions with strain. The softening process within ferrite was classified as "extended DRV", characterised by a continuous increase in misorientations across the sub-boundaries with strain, for both deformation temperatures.

The microstructure evolution and softening processes during high-temperature deformation of a 21Cr-10Ni-3Mo duplex stainless steel

The austenite and ferrite microstructure evolution and softening mechanisms have been investigated in a 21Cr-10Ni-3Mo duplex stainless steel, containing about 60% austenite, deformed in torsion at 1200°C using a strain rate of 0.7 s-1. The above experimental conditions led to the formation of a small volume fraction of new austenite grains through discontinuous dynamic recrystallization (DDRX), which could not account for the observed large softening on the flow curve. DDRX grains mainly formed through the strain-induced migration of the pre-existing austenite grain boundaries, known to dominate in single-phase austenite, complemented by subgrain growth in the interface regions with ferrite. A significant portion of austenite dynamic softening has been attributed to the large-scale subgrain coalescence, the extent of which increased with strain, which seems to have contributed substantially to the observed flow stress decrease. The above process thus appears to represent an alternative mode of austenite dynamic softening to the classical DDRX in the duplex austenite/ferrite microstructure, characterised by limited availability of the pre-existing austenite/austenite high-angle boundaries, deformed at a high temperature. The softening mechanism within ferrite has been classified as "continuous DRX", characterised by a gradual increase in misorientations between neighbouring subgrains with strain and resulting in the progressive conversion of subgrains into "crystallites" bounded partly by low-angle and partly by large-angle boundaries.

A heuristic model selection scheme for representing hot flow data using the hot torsion test results

The problem of "model selection" for expressing a wide range of constitutive behaviour adequately using hot torsion test data was considered here using a heuristic approach. A model library including several nested parametric linear and non-linear models was considered and applied to a set of hot torsion test data for API-X 70 micro-alloyed steel with a range of strain rates and temperatures. A cost function comprising the modelled hot strength data and that of the measured data were utilized in a heuristic model selection scheme to identify the optimum models. It was shown that a non-linear rational model including ten parameters is an optimum model that can accurately express the multiple regimes of hardening and softening for the entire range of the experiment. The parameters for the optimum model were estimated and used for determining variations of hot strength of the samples with deformation.

A non-associated plasticity model with anisotropic and nonlinear kinematic hardening for simulation of sheet metal forming

A material model for more thorough analysis of plastic deformation of sheet materials is presented in this paper. This model considers the following aspects of plastic deformation behavior of sheet materials: (1) the anisotropy in yield stresses and in work hardening by using Hill's 1948 quadratic yield function and non-constant stress ratios which leads to different flow stress hardening in different directions, (2) the anisotropy in plastic strains by using a quadratic plastic potential function and non-associated flow rule, also based on Hill's 1948 model and r-values, and (3) the cyclic hardening phenomena such as the Bauschinger effect, permanent softening and transient behavior for reverse loading by using a coupled nonlinear kinematic hardening model. Plasticity fundamentals of the model were derived in a general framework and the model calibration procedure was presented for the plasticity formulations. Also, a generic numerical stress integration procedure was developed based on backward-Euler method, so-called multi-stage return mapping algorithm. The model was implemented in the framework of the finite element method to evaluate the simulation results of sheet metal forming processes. Different aspects of the model were verified for two sheet metals, namely DP600 steel and AA6022 aluminum alloy. Results show that the new model is able to accurately predict the sheet material behavior for both anisotropic hardening and cyclic hardening conditions. The drawing of channel sections and the subsequent springback were also simulated with this model for different drawbead configurations. Simulation results show that the current non-associated anisotropic hardening model is able to accurately predict the sidewall curl in the drawn channel sections.