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In order to predict the failure of AZ31B Mg sheet at room temperature under uniaxial and biaxial loading paths, analytical expressions based on the maximum shear stress criterion in conjunction with the quadratic anisotropic yield function and plastic potential were developed. By utilizing the formulations based on the associated flow rule (AFR) and the non-associated flow rule (NAFR), different levels of material anisotropy were considered with the developed equations. Material coefficients of anisotropy were obtained from tensile and bulge tests taking into account the differential work hardening of AZ31B Mg sheet. Failure predictions were performed and compared with the experimental failure strains measured by the hemispherical dome tests at room temperature. In the failure prediction of AZ31B Mg sheet, it was found that the material anisotropy and the differential work hardening exhibited by the AZ31B Mg sheet were primary factors which have a major influence on the results of failure prediction, and the formulations based on the NAFR with the material coefficients obtained by taking into account the differential work hardening showed good accuracy by yielding failure predictions close to the experimentally measured failure strains.

s In this work, the qualCONVERSION(0ities of sheet formability (i.e., stretchability and drawability), of twinning-induced plasticity (TWIP), steel-cored thr$ee-layer steel sheets were investigated in terms of tensile parameters (i.e., strain hardening exponent, strain rate sensitivity, normal anisotropy, mean R -value, and total elongation). The tensile parameters of TWIP steel-cored three-layer steel sheets follow the force-based rule of mixtures. The limit drawing ratio, the measure of drawability, of the three-layer steel sheet was proportional to the mean R -value and the strain rate sensitivity while the limit dome height (LDH), the measure of stretchability, could not be correlated with any tensile parameters. The LDH of the TWIP steel-cored layer sheet was superior to that of the single layer due to the inhibition of serration in the TWIP steel-core during the Erichsen test.

This paper is concerned with modeling of fracture-based forming limit criteria for anisotropic materials in sheet metal forming to predict the sudden fracture in complicated forming processes. The Lou–Huh ductile fracture criterion is modified using the Hill's 48 anisotropic yield function instead of the von Mises isotropic yield function to take account of the influence of anisotropy on the equivalent plastic strain at the onset of fracture. For the derivation of an anisotropic ductile fracture criterion, the principal stresses (σ1,σ2,σ3) are expressed in terms of the stress triaxiality, the Lode parameter, and the equivalent stress (ηH,LP,σ¯H) based on the Hill's 48 yield function. Three different kinds of fracture-based forming limit criteria are suggested and investigated with an assumption that the stress state is under the plane stress condition with proportional loading. To determine the parameters of the model proposed, the two-dimensional digital image correlation (2D-DIC) method is utilized to measure the strain histories on the surface of three different types of specimens during deformation and the measurement results are investigated to identify the anisotropy effect on the equivalent plastic strain at the onset of fracture. This paper also discusses about a scaling method for a strain-based fracture forming limit criterion in order to capture the onset of fracture using a single forming limit curve for an anisotropic material. From the comparison of various forming limit criteria suggested, it is concluded that a polar effective plastic strain-based (PEPS) fracture forming limit diagram (FFLD) is suitable for prediction of the sudden fracture in AHSS sheets in complicated sheet metal forming processes on the basis of its path independence and simplicity of measuring strains in real forming processes.

Residual stress effect of the deep drawn TWIP steel on delayed fracture was investigated. Microstructural features of the TWIP steels did not change after stress relief annealing, while the elastic lattice strain dropped to 0.0007. Delayed fracture of the drawn TWIP steel occurred after 203 hours of HCl immersion testing, but did not occur in the annealed one. It is clear that residual stress after the drawing is the primary reason for the delayed fracture of TWIP steels.

Although the compact endless cast and rolling mill (CEM) is a promising candidate as a next-generation energy-saving steel process, due to its short history, the formability of the steel sheet produced by the CEM process are not known yet. Herein, drawability and stretchability of low-carbon steel sheets produced by the CEM process are investigated and compared with those of conventional hot-rolled low-carbon steel sheets, to estimate its applicability to industrial parts. Finite element analyses using the Gurson-Tvergaard-Needleman damage model were conducted and compared with the experimental results. Homogeneous microstructure and relatively strong textures of {111}||ND γ-fibers and 〈110〉||RD α-fibers were developed in the CEM-processed steel in comparison with the conventional hot-rolled specimen. The drawn cup of the CEM specimen showed weak earing phenomena, while having higher limiting drawing ratios (2.0 and 1.95 in the experimental and numerical simulation, respectively). Furthermore, a difference in limit dome height between the two specimens is negligible. Therefore, it is confirmed that CEM-processed steels have comparable properties of strength and formability, provide an effective manufacturing process, and exhibit good potential as a next-generation energy-saving process.

Herein, we report the results of our experimental and computational investigation of the deep drawing behavior of twinning-induced plasticity (TWIP)-cored three-layer steel sheet. Various directional tensile tests for monolayer sheets of the TWIP and low-carbon (LC) steels were performed for evaluation of flow curves and anisotropic coefficients, which are used as input data of the finite element analyses for deep drawing of the monolayer and three-layer sheets. The experimental deep drawing behaviors of the layered sheets of three thickness ratios, and of the monolayer sheets, are computationally analyzed in terms of earring and variations of local thickness along the positions in the drawn cups. It was found that the three-layer sheets are more planar-isotropic in the sense of earring than the monolayer sheets, even more than the TWIP steel sheet. The thickness uniformity along the initial radial direction in the layered sheets is in between the heterogeneous TWIP steel and the relatively homogeneous LC steel. The present results shed light on the future direction of development of steel sheets with planar-isotropic and homogeneous deep-drawing characteristics.

Stretch-flangeability representing the capability of a sheet material to form into a complex shaped part is not a well-known sheet metal forming property. We correlate mechanical properties with stretch-flangeability of various advanced high strength steels (AHSSs) to capture the stretch-flanging phenomenon and improve the stretch-flangeability of steel sheet materials. The stretch-flangeability of materials is usually evaluated using a hole expansion test. During the hole expansion test, the stress state in the hole edge part of the specimen is almost the same as that of the uniaxial tensile test. However, a single parameter in tensile properties of the AHSSs exhibits no clear correlation with flangeability estimated as the hole expansion ratio (HER). Because micro-cracks in the hole edge region of the hole expansion testing samples play a significant role in HER values, we propose and demonstrate that fracture toughness is the key factor governing the HER of AHSSs.

Martensitic steels are widely used for safety parts in automobiles due to their high strength and excellent energy absorption, in particular, under high strain-rate service conditions. Precipitation in the martensite matrix increases strength but reduces ductility, limiting the application of martensitic steels for parts with complex shapes. In this study, the bending behavior of TiN particle-reinforced martensitic steel was investigated using a micro-digital image-correlation technique. The strain distribution of deformed martensitic steel induces deformation localization in lath martensite and crack initiation in the TiN particles. Cracks in TiN particles occurred within local strain ranges of 0.2–5.7% in particles of diverse size. Such cracked particles act as sites of void nucleation and growth, and the cracks generated, then propagate in the martensite packets. This result shows that TiN-particle cracking is the critical factor affecting the ductility and bendability of martensitic steel.

While cast magnesium components have been extensively used in the automotive industry, only niche applications are known to exist for magnesium sheets to this date. This is believed to originate from limitations in the material property spectrum covered by existing alloys. By utilising the twin-roll casting technique, novel Mg–Zn–Ca–Zr (ZXK) alloy sheets can be developed with improved formability as a result of a texture weakening effect. More importantly, it can be shown that these new alloy sheets can be processed at industrial scale. Based on the magnesium-specific design of a Volkswagen Passat decklid, the advantages of these new highly formable sheets in an automotive production environment can be evaluated.

The main objective of this work is to experimentally and numerically evaluate the macro-performance of the automotive TWIP (twinning induced plasticity) sheet in conjunction with formability. In order to characterize the mechanical properties, the simple tension and compression tests were performed for anisotropic properties, while the strain rate test was carried out to evaluate strain rate sensitivity. The forming limit diagram was measured and incorporated into the simulation program, while the theoretical prediction of the diffuse and localized necking was also carried out utilizing Hill’s and the M–K theories as well as Dorn’s and Swift’s diffuse theories. Note that the generalized criteria of Hill’s, Dorn’s and Swift’s theories were derived for general anisotropic sheets as well in this work. For numerical simulations, the anisotropic yield functions Yld2000-2d and Hill48 as well as the isotropic Mises yield function were selectively applied along with the isotropic hardening law. Formability verification was performed, utilizing Yld2000-2d, for the hemispherical dome stretching, notch and simple tension tests with specimens selectively prepared by milling and punching, while anisotropic properties were verified through the three point bending and cylindrical cup drawing tests, comparing the performance of the three yield functions.

In an effort to reduce the weight of vehicles, automotive companies are replacing conventional steel parts with light weight alloys and/or with advanced high strength steels (AHSS) such as dual-phase (DP), twinning induced plasticity (TWIP), and transformation induced plasticity (TRIP) steels. The main objective of this work is to experimentally and numerically evaluate the macro-performance of the automotive TWIP sheet in conjunction with springback. In order to characterize the mechanical properties, simple tension and tension-compression tests were performed to determine anisotropic properties, as well as the Bauschinger, transient, and permanent softening behaviors during reverse loading. For numerical simulations, the anisotropic yield function Yld2000-2d was utilized along with the combined isotropic-kinematic hardening law based on the modified Chaboche model. Springback verification was performed for the unconstrained cylindrical bending and 2D draw bending tests.

In this paper, the finite element method (FEM) was applied to analyze the plastic flow and strain hardening behavior of pure copper, subjected to rotary-die equal channel angular pressing (RD-ECAP) up to four passes. The die was rotated 90° counter clockwise between the passes in the simulation. The effective strain distribution and load–stroke curves were investigated. The load was increased with the number of rotary-die equal channel angular pressing passes. The results show that, plastic deformation becomes inhomogeneous with the number of passes due to an end effect, which was not found seriously in conventional equal channel angular pressing (ECAP). Especially, decreasing corner gap with increasing the number of passes was observed and explained by the strain hardening effect.

Equal channel angular pressing (ECAP) is so far the most viable severe plastic deformation procedure to extrude material by using specially designed channel dies without any substantial changes in geometry and to prepare an ultrafine grained material. Magnesium is the lightest of all structural metallic materials, but a typical hard-to-deform metallic material due to its HCP structure and associated slip systems. ECAP has been applied for a processing method of severe plastic deformation to achieve grain refinement of magnesium and to enhance it's low ductility. In particular, we investigated the deformation and fracture behavior of pure magnesium workpiece using experimental and numerical methods. The finite element method with different ductile fracture models was employed to simulate plastic deformation and fracture behavior of the workpiece.

In this paper, grain refinement of pure magnesium using severe plastic deformation was investigated in order to enhance mechanical properties of the hard-to-deform metallic material. The microstructure and the mechanical properties of Mg processed by equal channel angular pressing (ECAP) at various processing temperatures were examined experimentally. ECAP of channel angle of 90 � and corner angle of 0 � was successful without fracture of the magnesium workpiece at 300 � C, but not under 200 � C. The hardness of the ECAP processed magnesium decreased with increasing ECAP processing temperature. The effect of temperature on the hardness, instrumented indenting response and microstructure of the ECAP processed magnesium were discussed. Fracture behavior during ECAP under different processing temperatures was demonstrated using the finite element method associated with ductile fracture model. [doi:10.2320/matertrans.MC200725]

Although equal channel angular pressing (ECAP), imposing large plastic shear strain deformation by moving a workpiece through two intersecting channels, is a promising severe plastic deformation method for grain refinement of metallic materials, its batch type characteristic makes ECAP inefficient for multiple-passing. Rotary-die ECAP (RDECAP) proposed by Nishida et al. can achieve high productivity by using continuous processing without taking out the samples from the channel. However, plastic deformation behavior during RD-ECAP has not been investigated. In this study, material plastic flow and strain hardening behavior of the workpiece during RD-ECAP was investigated using the finite element method. It was found that plastic deformation becomes inhomogeneous with the number of passes due to an end effect, which was not found seriously in ECAP. Especially, decreasing corner gap with increasing the number of passes was observed and explained by the strain hardening effect.

Preform design is an effective means of achieving the homogeneous deformation of workpiece materials and decreased load in metal forming. However, this approach has not been applied to equal channel angular pressing (ECAP). In this paper, the plastic deformation behavior of workpieces having three different preform shapes during ECAP was investigated using experimental and finite element analyses. The results indicated that a preform design slant at the back part of the workpiece head is beneficial to homogeneous deformation, reducing the maximum pressing load at the initial stage and eliminating folding defects at strain concentration points.

In order to analyze the creep behaviour of Cr-Mo steels, an elasto-viscoplastic constitutive model based on dislocation density considerations is described. A combination of a kinetic equation, which describes the mechanical response of a material at a given microstructure in terms of dislocation glide, and evolution equations for internal variables characterising the microstructure provide the constitutive equations of the model. Microstructural features of the material are implemented in the constitutive equation. The internal variables are associated with the total dislocation density. The model has a modular structure and can be adjusted to describe a particular type of materials behaviour and metal forming processes. In this paper, the predicted creep behaviour of Cr-Mo steels is compared with the experimental results.

Equal channel angular pressing (ECAP) is a viable forming procedure to extrude material by use of specially designed channel dies without a substantial change in geometry and to make an ultrafine grained material by imposing severe plastic deformation. Because the evolution of microstructures and the mechanical properties of the deformed material are directly related to the amount of plastic deformation, the understanding of the phenomenon associated with strain development is very important in the ECAP process. The plastic deformation behaviour during pressing is governed mainly by die geometry (channel sizes, a channel angle and corner angles), material properties (strength and hardening behaviour) and process variables (temperature, lubrication and deformation speed). There is a need for modelling techniques which may permit a wider study of the effects observed for better process control and the understanding of process related phenomena. In this study, we describe a range of our continuum modelling results of the ECAP process in order to illustrate the modelling applicability. Firstly, the finite element results of ECAP modelling for various geometric factors are described. Secondly, the inhomogeneous deformation due to the hardening property of the material is explained. Lastly, modelling the temperature field coupled with stress as a typical process variable in ECAP is presented.

In recent years, equal channel angular pressing (ECAP) has been the subject of intensive study in recent years due to its capability of producing fully dense samples having a ultrafine grain size. In this process, knowledge of the internal stress, strain and strain rate distribution is fundamental to the determination of the optimum process conditions for a given material. The properties of the ECAPed materials are strongly dependent on the shear plastic deformation behavior during ECAP, which is controlled mainly by die geometry, material properties, and process conditions. In this study, we applied the finite element method to obtain a better understanding the plastic deformation behavior of the workpiece during ECAP in terms of material flow properties and die geometries. The material flow stress, i.e. hardening behavior, was considered to be both strain rate dependent and strain dependent. The deformation within the workpiece is inhomogeneous unlike the ideal pure shear deformation. The mesh size dependence on the local deformation behavior in the deforming zone was addressed. The corner gap formation between the die and workpiece during the plane strain ECAP process was investigated. The mechanism of the corner gap formation is described in conjunction with the hardening behavior and local flow velocity of the workpiece in the deforming zone.

Severe plastic deformation (SPD) methods have been the subject of intensive investigation in recent years not only due to the superior physical and mechanical properties inherent to various ultrafine-grained materials, but also to several advantages of severely plastic-deformed materials compared to nano-structured materials manufactured by other methods through powder forms. Among various severe plastic deformation methods, equal channel angular pressing (ECAP), which involves a large simple shear plastic deformation by moving a workpiece through two intersecting channels has been the subject of intensive study due to its capability of producing fully dense samples containing ultrafine grain size. In this process, knowledge of the plastic deformation behaviour of the workpiece during the process is very important for the determination of the optimum process conditions such as die design, speed, temperature, friction and preform design. In this study, the rigid–plastic two-dimensional finite element method using the DEFORM2D code is presented for the better understanding of the plastic deformation behaviour of the workpiece. The material flow stress is considered to be the strain rate and strain dependant. The deformation within the workpiece is inhomogeneous unlike the ideal pure shear deformation. The pressed workpiece is divided into three zones (front, steady and end zones). It was also found that a lesser shear deformation zone occurs in the outer part of the workpiece, which is attributed to the faster flow of the outer part compared to the inner part within the main deformation zone. In particular, inhomogeneous deformation of the workpiece with respect to the effect of the friction factor is investigated.

The effects of strain hardenability and strain rate sensitivity on the plastic flow and deformation inhomogeneity during equal channel angular pressing were studied using a finite element method analysis. In this study, perfect plastic nonhardening and rate-insensitive materials, and rate-sensitive materials were considered. In case of the nonhardening and rate-insensitive materials, the deformed geometry was predicted to be quite uniform and homogeneous. Deformation inhomogeneity developed, however, in materials with finite work-hardening exponent and strain-rate sensitivity. The corner gap formed in strain-hardening materials whereas the upper and lower channel gaps formed in strain-rate-sensitive materials. The deformation inhomogeneity was strongly dependent on the relative effects of strain-hardening exponent and strain-rate sensitivity. The predictions on the deformation inhomogeneity and the formation of corner and channel gaps were compatible with the experimental data published in the literature.

A die internal corner gap is usually found during equal channel angular pressing (ECAP) of materials. Finite element analysis using the DEFORM2D code is carried out in order to investigate the corner gap formation between the die and workpiece during the plane strain ECAP process. The comparison of the deformation and the corner gap formation behaviour between the strain hardening material and the quasi-perfect plastic material was made. The mechanism of the corner gap formation is described in conjunction with the strain hardening behaviour and local flow velocity of the workpiece in the deforming zone. The adjustment of the corner angle from the die corner angle to the arc curvature of the workpiece is necessary for a better prediction of the strain during ECAP.