Plastic Strain Path Research Articles

Correction: Influence of Plastic Anisotropy and Strain Path on strain-induced Phase Transformation of Cobalt

Correction: Influence of Plastic Anisotropy and Strain Path on strain-induced Phase Transformation of Cobalt

Influence of Plastic Anisotropy and Strain path on strain-induced Phase Transformation of Cobalt

Influence of Plastic Anisotropy and Strain path on strain-induced Phase Transformation of Cobalt

Effect of loading-path on the elastic modulus degradation of high strength steels

Experiments of repetitive uniaxial tension are performed for DP590, TRIP590, TRIP780, and BH220 steels. Variation of chord modulus of the four materials with accumulated plastic strain is discussed. Large specimens of uniaxial tension, wide plate tension and cruciform tension are prestrained in different plastic strain. Uniaxial tension of sub-size samples which are machined from the prestrained large specimens is performed. Dependence of the normalized chord modulus of the four metals on strain path is discussed in detail. The results show that elastic modulus degradation is dependent on the material strength, accumulated plastic strain and strain path. At the same equivalent strain, the chord modulus degradation of TRIP780, TRIP590, DP590, BH220 steels decreases in turn. The chord modulus of TRIP780 steel at 0.24 equivalent strain reaches 20.5%. The chord modulus of DP590 steel is more sensitive to strain path change than the other three metals. The path of biaxial stretching combined with uniaxial tension provides the greatest chord modulus degradation among the six loading paths. Each material should have the most suitable loading path under which the elastic modulus variation can be minimized so springback can be easily controlled.

Numerical research on springback law of tension-compression yield asymmetry sheet in multi-point forming

Springback of SUS430/AA1050/TA1 (SAT) laminated sheet in multi-point forming (MPF) is difficult to predict due to its complex microstructure. In this work, the polycrystalline texture and crystal structure of the three materials were measured firstly by electron backscatter diffraction (EBSD). Crystal plasticity finite element method (CPFEM) considering twinning and slip was used to predict the anisotropy and tension-compression yield asymmetry (TCYA) of the materials. The data obtained by virtual simulation are validated and used to calibrate the phenomenological yield criteria. In the springback prediction model, the three materials were modeled using the layered modeling method. The anisotropic yield criteria were implemented into finite element software ABAQUS via a user-defined material subroutine VUMAT to fully consider the anisotropy of the SAT laminated sheet. The comparison between the forming experiment and simulation results shows that the model can predict the springback accurately. Finally, the effect of plastic deformation, strain path, and TA1 layer thickness on springback were discussed.

Transformation of a rolling mill aggregate to a cyber physical production system: from sensor retrofitting to machine learning

This paper describes the transformation of a rolling mill aggregate from a stand-alone solution to a fully integrated cyber physical production system. Within this process, already existing load cells were substituted and additional inductive and magnetic displacement sensors were applied. After calibration, those were fully integrated into a six-layer digitalization architecture at the Smart Forming Lab at the Chair of Metal Forming (Montanuniversitaet Leoben). Within this framework, two front end human machine interfaces were designed, where the first one serves as a condition monitoring system during the rolling process. The second user interface visualizes the result of a resilient machine learning algorithm, which was designed using Python and is not just able to predict and adapt the resulting rolling schedule of a defined metal sheet, but also to learn from additional rolling mill schedules carried out. This algorithm was created on the basis of a black box approach, using data from more than 1900 milling steps with varying roll gap height, sheet width and friction conditions. As a result, the developed program is able to interpolate and extrapolate between these parameters as well as different initial sheet thicknesses, serving as a digital twin for data-based recommendations on schedule changes between different rolling process steps. Furthermore, via the second user interface, it is possible to visualize the influence of this parameters on the result of the milling process. As the whole layer system runs on an internal server at the university, students and other interested parties are able to access the visualization and can therefore use the environment to deepen their knowledge within the characteristics and influence of the sheet metal rolling process as well as data science and especially fundamentals of machine learning. This algorithm also serves as a basis for further integration of materials science based data for the prediction of the influence of different materials on the rolling result. To do so, the rolled specimens were also analyzed regarding the influence of the plastic strain path on their mechanical properties, including anisotropy and materials’ strength.

Investigating formability enhancement in double side incremental forming by developing a new test method of tension under cyclic bending and compression

Incremental sheet forming (ISF), including single point incremental forming (SPIF) and double side incremental forming (DSIF), has demonstrated significantly enhanced material formability compared to traditional sheet metal forming processes. However, the material deformation mechanisms that lead to the enhanced formability in DSIF are not fully understood. In this study, a new test method, named as Tension under Cyclic Bending and Compression (TCBC), has been developed to investigate four deformation modes observed in DSIF, including tension, compression, bending and cyclic loading, on the material formability enhancement. An analytical model based on the elementary plasticity theory has been developed to characterize the effect of tension, compression, bending and cyclic loading on the initiation of material plastic deformation. A TCBC rig has been manufactured and experimental tests of two aluminium alloys have been conducted by applying the Design of the Experiments to investigate the significant effects of different deformation modes on the material formability. Finite element modelling of TCBC test as well as DSIF process has also been developed to compare their plastic strain evolution and strain paths during the cyclic deformation process. The material formability has been found to be improved significantly under TCBC condition and the existence of compression loading leads to strengthened localized material plastic deformation, which contributes to the enhanced material formability and delayed fracture. The new TCBC test method developed in this study has demonstrated its potential to replace the current testing method using the DSIF process itself for material formability studies.

Martensitic transformation of an austenitic stainless steel under non-proportional cyclic loading

In this study, a series of cyclic tests on a 304L stainless steel with different loading paths were conducted. It revealed that as the non-proportionality of loading path increased, the growth rate of martensitic content became higher and its distribution among the austenitic matrix appeared more uniform. A phase transformation kinetics equation was modified to describe the effect of cumulative plastic strain, loading amplitude and loading path on martensitic transformation. A stress decomposition rule was proposed to incorporate both the non-proportional hardening and martensitic transformation hardening to describe the hardening mechanism.

Formability prediction of advanced high-strength steel sheets by means of combined experimental and numerical approaches

Abstract In this work, a group of four capable prediction tools—Classical Forming Limit Curve (FLC), Forming Limit Stress Curve (FLSC), Damage Curve (DC) associating stress-triaxiality with plastic strain and Nonlinear Strain Path Forming Limit Curve (nonlinear strain path FLC) based on an innovative punch originally designed by the Institute for Metal Forming Technology (IFU), University of Stuttgart—are employed to evaluate formability of DP590 advanced high-strength steel (AHSS). The results are subsequently compared. A classical FLC is created with restriction to the Nakajima stretching-test guideline, in which a 100-Tonne universal tensile testing machine is operated to press 1-mm thick DP590 sheets. A nonlinear strain path FLC is generated with an application of an IFU-designed punch to realise nonlinear strain paths under a particular standardised Nakajima testing environment. A stress-based FLC is computationally obtained by transforming the classical FLC, realised in a major-minor strain space, into an FLSC in a principal-stress space using the Hill’48 yield criterion equipped with the Swift strain-hardening law. A DC is arithmetically determined through a combination of the plastic flow rule and Hill’48 yield criterion. To verify and compare those gained curves, both hole-expansion and Fukui stretch-drawing tests are conducted both experimentally and numerically. Regarding the simulation model for numerical investigation, material flow behaviour and deformation anisotropy are modelled by the Swift hardening law and Hill’48 yield criterion, respectively. This research has once again proved that FLSC, DC and nonlinear strain path FLC can obviously identify the forming limit of DP590 AHSS more realistically than the classical FLC can.

On the use of tensor paths to estimate the nonproportionality factor of multiaxial stress or strain histories under free-surface conditions

Nonproportional (NP) strain hardening is caused by multiaxial load histories that induce variable principal stress/strain directions, activating cross-slip bands in several directions, due to the associated rotation of the maximum shear planes. This effect increases the strain-hardening behavior observed under proportional loads, those with fixed principal directions, and must be considered in multiaxial fatigue calculations, especially for materials with low stacking fault energy, such as austenitic stainless steels. NP hardening depends on the material and on the shape of the multiaxial load history path in a stress or strain diagram as well. It can be evaluated by a nonproportionality factor \({F_{\rm NP}}\) that varies from zero, for a proportional load history, to one, for a \({90^{\circ}}\) out-of-phase tension–torsion loading with the same normal and effective shear amplitudes. Originally, \({F_{\rm NP}}\) was estimated from the aspect ratio of a convex enclosure that contains the load history path, such as an ellipse or a prismatic enclosure, but such convex enclosure estimates can lead to poor predictions of \({F_{\rm NP}}\). Another approach consists on evaluating the shape of the six-dimensional (6D) path described by the six normal and shear components of the stress tensor, where the stress path contour is interpreted as a homogeneous wire with unit mass. The moment of inertia (MOI) tensor of this hypothetical wire is then calculated and used to estimate \({F_{\rm NP}}\). The use of 6D stress paths to estimate \({F_{\rm NP}}\) is questionable, since 6D formulations implicitly include the effect of the hydrostatic stress, while NP hardening is caused by the deviatoric plastic straining, not by stresses alone or by their hydrostatic component. In this work, the NP factor \({F_{\rm NP}}\) of a multiaxial load history is estimated from the eigenvalues of the MOI tensor of the plastic strain path, which are associated with the accumulated plastic straining in the principal directions defined by the associated eigenvectors. The presented formulation assumes free-surface conditions, but allows a surface pressure, covering the conditions of most critical points, which indeed are located on free surfaces. Experimental results for 14 different tension–torsion multiaxial histories prove the effectiveness of the proposed method.

Non-proportional hardening models for predicting mean and peak stress evolution in multiaxial fatigue using Tanaka’s incremental plasticity concepts

Non-proportional (NP) hardening can have a significant effect on multiaxial fatigue lives due to the increase in mean and peak stresses it can cause when compared to proportional loads of similar range. Its effect depends both on the material and on the load history path, quantified respectively by the additional NP hardening coefficient αNP and the NP factor FNP. However, since FNP depends on the load path, it is not easy to evaluate under complex multiaxial loading conditions. So, several estimates for the steady-state value of FNP have been proposed to deal with such cases, based on enclosing ellipses or on integrals calculated along the stress, strain, or plastic strain path. Tanaka’s incremental plasticity model, on the other hand, is able to predict the NP hardening evolution as a function of the accumulated plastic strain p along any load history, based on the concept of a polarization tensor [PT] that can be correlated to an internal dislocation structure. In this work, it is shown that the eigenvectors of [PT] represent principal directions along which dislocation structures may form, whose intensity is quantified by the respective eigenvalues. Two new integral estimates for the steady-state FNP of periodic load histories are proposed, one that exactly reproduces the incremental plasticity predictions from Tanaka’s model, and a simpler version calculated solely as a function of the eigenvalues of [PT]. Both can be readily used in fatigue design to correctly account for the additional mean or peak stress effects induced by NP periodic histories. For general non-periodic multiaxial histories, it is also shown that Tanaka’s model can be expressed as an evolution equation for FNP(p). Tension–torsion experiments with 316L steel tubular specimens under especially selected discriminating square NP strain paths are conducted to validate the proposed models.

Microstructural evolution of nanolayered Cu–Nb composites subjected to high-pressure torsion

Bulk nanolayered Cu/Nb composites fabricated by accumulative roll bonding (ARB), leading to a nominal layer thickness of 18nm, were subjected to large shear deformation by high-pressure torsion at room temperature. The evolution of the microstructure was characterized using X-ray diffraction, transmission electron microscopy and atom probe tomography. At shear strains of ∼4, the crystallographic texture started to change from the one stabilized by ARB, with a Kurdjumov–Sachs orientation relationship and a dominant {112}Cu||{112}Nb interface plane, toward textures unlike the shear texture of monolithic Cu and Nb. At larger strains, exceeding 10, the initial layered structure was progressively replaced by a three-dimensional Cu–Nb nanocomposite. This structure remained stable with respect to grain size, morphology and global texture from strains of ∼290 to the largest ones used in this study, 5900. The three-dimensional self-organized nanocomposites comprised biconnected Cu-rich and Nb-rich regions, with a remarkably small coexistence length scale, ∼10nm. The results are discussed in the context of the effect of severe plastic deformation and strain path on microstructure and texture stability in highly immiscible alloy systems.

Studies of the Optimal Hardening Parameters in Sandy Soil Shear Hardening Constitutive Model

Through a series of drainage analysis of plane strain compression tests on the Toyoura sand under different stress path, we found that the plastic shear strain and stress path of great relevance. But due to that a yield locus represents a specific yield level and usually do not related with stress paths, the hardening parameter of the parametric should also has nothing to do with the stress path. This article based on the analysis of the laboratory test results, put forward a stress path-independent plastic shear strain energy modified function as shear yield hardening parameters. Then based on the above type of energy state function proposed to build a sandy soil elasto-plastic constitutive model, and compared with corresponding numerical calculation results to make an effective verification.

Studies of the Optimal Hardening Parameters in Sandy Soil Shear Hardening Constitutive Model

Through a series of drainage analysis of plane strain compression tests on the Toyoura sand under different stress path, we found that the plastic shear strain and stress path of great relevance. But due to that a yield locus represents a specific yield level and usually do not related with stress paths, the hardening parameter of the parametric should also has nothing to do with the stress path. This article based on the analysis of the laboratory test results, put forward a stress path-independent plastic shear strain energy modified function as shear yield hardening parameters. Then based on the above type of energy state function proposed to build a sandy soil elasto-plastic constitutive model, and compared with corresponding numerical calculation results to make an effective verification.

Combined Model to Describe Both the Mechanical and Microstructural Transients under a Reversal of Strain

A strain reversal produces microstructural and mechanical transients that cannot be described with conventional models applicable under monotonic deformation conditions. State-of-the-art models incorporating plastic strain path effects are polarized into continuum constitutive models of cyclic plasticity and multiscale constitutive approaches extrapolating crystallographic hardening models for monocrystals to polycrystals. The present work proposes a model midway between these two approaches that describes the mechanical transient through a combined kinematic-isotropic hardening model and the microstructural transient and its effect on the subsequent static recrystallization kinetics. The incorporation of an effective strain concept makes the link among the different submodels and allows for the first time an accurate reproduction with a reduced number of parameters both for mechanical and microstructural experimental data during the transient following a strain reversal.

Disorders of body posture at women after mastectomy in photogrametric estimation

A polycrystalline aluminum sample with a quasi-2D single layer of coarse grains is plastically deformed in a channel die plane strain set-up at ambient temperature and low strain rate. The microtexture of the specimen is determined by analysis of electron back scattering patterns obtained in a scanning electron microscope. The spatial distribution of the plastic microstrains at the sample surface is determined by measurement of the 3D plastic displacement field using a photogrametric pixel-based pattern recognition algorithm. The initial microtexture is mapped onto a finite element mesh. Continuum and crystal plasticity finite element simulations are conducted using boundary conditions which approximate those of the channel die experiments. The experimental and simulation data are analyzed with respect to macromechanical and micromechanical effects on grain-scale plastic heterogeneity. The most important contributions among these are the macroscopic strain profile (friction), the kinematic hardness of the crystals (individual orientation factors), the interaction with neighbor grain, and grain boundary effects. Crystallographic analysis of the data reveals two important points. First, the macroscopic plastic strain path is not completely altered by the crystallographic texture, but modulated following soft crystals and avoiding hard crystals. Second, grain-scale mechanisms are strongly superimposed by effects arising from the macroscopic profile of strain. The identification of genuine interaction mechanisms at this scale therefore requires procedures to filter out macroscopically induced strain gradients. As an analysis tool, the paper introduces a micromechanical Taylor factor, which differs from the macromechanical Taylor factor by the fact that crystal shear is normalized by the local rather than the global von Mises strain.

209 多結晶金属におけるねじりを含む塑性変形経路に伴う表面あれ形態の変化

209 多結晶金属におけるねじりを含む塑性変形経路に伴う表面あれ形態の変化

Micromechanical and macromechanical effects in grain scale polycrystal plasticity experimentation and simulation

A polycrystalline aluminum sample with a quasi-2D single layer of coarse grains is plastically deformed in a channel die plane strain set-up at ambient temperature and low strain rate. The microtexture of the specimen is determined by analysis of electron back scattering patterns obtained in a scanning electron microscope. The spatial distribution of the plastic microstrains at the sample surface is determined by measurement of the 3D plastic displacement field using a photogrametric pixel-based pattern recognition algorithm. The initial microtexture is mapped onto a finite element mesh. Continuum and crystal plasticity finite element simulations are conducted using boundary conditions which approximate those of the channel die experiments. The experimental and simulation data are analyzed with respect to macromechanical and micromechanical effects on grain-scale plastic heterogeneity. The most important contributions among these are the macroscopic strain profile (friction), the kinematic hardness of the crystals (individual orientation factors), the interaction with neighbor grain, and grain boundary effects. Crystallographic analysis of the data reveals two important points. First, the macroscopic plastic strain path is not completely altered by the crystallographic texture, but modulated following soft crystals and avoiding hard crystals. Second, grain-scale mechanisms are strongly superimposed by effects arising from the macroscopic profile of strain. The identification of genuine interaction mechanisms at this scale therefore requires procedures to filter out macroscopically induced strain gradients. As an analysis tool, the paper introduces a micromechanical Taylor factor, which differs from the macromechanical Taylor factor by the fact that crystal shear is normalized by the local rather than the global von Mises strain.

Three-Dimensional Evaluation of Free Surface Roughening Topography of Aluminum Sheet during Various Plastic Strain Paths.

Three-Dimensional Evaluation of Free Surface Roughening Topography of Aluminum Sheet during Various Plastic Strain Paths.

Plastic work and strain paths: the common geometric basis with phase stability

The paper shows by a graphical method that the path, between two states of homogenous deformation that minimises plastic work, is a straight line in the principal strain space between the two states. The method is valid for the condition that the same triad of material fibres remains mutually orthogonal throughout the deformation. The material deformed is considered to be rigid/hardening with a convex yield surface. Using a procedure very similar to that used to show the stability of a solution, it is shown that a straight line path results in less plastic work than two non collinear straight lines paths between the same points. By considering any path to be made up of infinitesimally small linear paths, this result is extended for any arbitrary path.

205 種々の塑性ひずみ経路におけるアルミニウムの表面あれ成長(機械材料・材料加工II)

205 種々の塑性ひずみ経路におけるアルミニウムの表面あれ成長(機械材料・材料加工II)