Jon Alkorta

A comparison of FEM and upper-bound type analysis of equal-channel angular pressing (ECAP)

Abstract In this paper the pressures needed for non-friction equal-channel angular pressing (ECAP) of perfectly plastic or strain-hardening materials are analysed using analytical approximations (upper-bound type) and numerical (finite-elements) methods. The approximate solutions agree very well with the FEM results for different ECAP die angles or materials. The convenience of using back-pressure for improving the strain pattern homogeneity of deformed strain-hardening materials is highlighted.

Hall-Petch Relationship of a TWIP Steel

The grain size dependence of the tensile properties of a TWIP steel has been determined for a wide range of grain sizes obtained by grain growth after complete recrystallization of cold rolled material. The near-linear stress-strain behaviour typical of either TWIP steels or other materials that deform by twinning has been observed, the work hardening rate being larger for the smaller grain sizes. The Hall-Petch slope increases as a function of strain, from 350 MPa μm1/2 for the yield stress to 630 MPa μm1/2 for the maximum uniform strain in the tensile tests, ε  0.40. Profuse twinning is observed in deformed specimens by means of FIB-ISE.

Limits of simulation based high resolution EBSD.

High resolution electron backscattered diffraction (HREBSD) is a novel technique for a relative determination of both orientation and stress state in crystals through digital image correlation techniques. Recent works have tried to use simulated EBSD patterns as reference patterns to achieve the absolute orientation and stress state of crystals. However, a precise calibration of the pattern centre location is needed to avoid the occurrence of phantom stresses. A careful analysis of the projective transformation involved in the formation of EBSD patterns has permitted to understand these phantom stresses. This geometrical analysis has been confirmed by numerical simulations. The results indicate that certain combinations of crystal strain states and sample locations (pattern centre locations) lead to virtually identical EBSD patterns. This ambiguity makes the problem of solving the absolute stress state of a crystal unfeasible in a single-detector configuration.

Microstructure and Indentation Size-Effect in Pure Niobium Subjected to SPD via ECAP and HPT

A commercially pure niobium has been subjected to SPD at room temperature ( ~0.11 TM) via ECAP (90º, route BC) up to 16 passes and via HPT up to shear strains γ =1000. ECAP-ed samples show an equiaxed structure after 8 and 16 passes with a decreasing average grain size. The results show that both the microstructure and mechanical properties of ECAP-ed samples do not reach a steady state up to at least 16 passes. HPT samples show at outer region a finer structural size but similar hardness values at similar equivalent strains. The nanoindentation results show an evident indentation size-effect even for the most deformed samples. The hardness values at the nano level converge for the recrystallized, the ECAP-ed and the HPT samples. This implies that, at the nano level, when the geometrically necessary dislocation density overcomes significantly the (initial) statistically stored dislocation density, hardness depends mainly on the physical intrinsic properties of the material (Burgers modulus, bulk modulus...) and the contribution of bulk mechanical properties (i.e., bulk yield strength) to hardness is smoothed down. Strain-rate sensitivity (SRS) of plastic strength has been also measured by means of rate-jump nanoindentation tests. The SRS is proportional to the inverse of hardness.

Improved simulation based HR-EBSD procedure using image gradient based DIC techniques

Conventional HR-EBSD is attracting much interest due to its ability of measuring relative crystal misorientations and microstresses with great accuracy. However, this technique needs the use of simulated patterns in order to get absolute values of crystal orientation and stresses and thus expand its use to intergranular analyses. Simulation-based approaches have shown many limitations due to the poor correlation with the real patterns specially when Bragg simulations are considered. This paper presents an improved algorithm based on gradient-based correlation techniques that makes simulation-based HR-EBSD possible. Based on this new algorithm, a new pattern center calibration procedure is proposed and validated. Also, a new hybrid procedure that combines simulation-based HR-EBSD with conventional HR-EBSD is presented that enables an absolute determination of both orientations and stresses with improved accuracy. The hybrid HR-EBSD is used to analyze the martensitic transformation induced by plastic deformation in an as-quenched Ti-12wt.%Mo alloy.

Towards a reliable procedure for the measurement of elastic modulus in instrumented indentation

Unloading stiffness is a critical magnitude when extracting elastic modulus in instrumented indentation. Any phenomenon which interacts with its measurement may affect the final calculation of the modulus. Analytical and numerical calculations have been carried out to determine the influence of thermal drift and creep response on its measurement, and the predictions were in good agreement with experimental results. Since the influence of thermal drift is depth-dependent, it determines the effective resolution of an indentation device for a given material. In contrast, indentation creep significantly alters unloading stiffness even for weakly rate-sensitive materials (sensitivity exponent, m < 0.05) but its effect could be smoothed down due to measurement artefacts (unloading curve fitting strategy). For instance, for an ultra-fine grained (UFG) pure niobium at room temperature (m ∼ 0.015 and H/Er ∼ 0.02), the error in the measurement of elastic modulus with a typical nanoindentation procedure (5 s of holding time and 65 s of unloading time) can be as high as 15%. This paper proposes simple rules for a reliable experimental procedure to avoid both thermal drift and creep effects on the measurement of elastic modulus, which are especially relevant for the new generation of high temperature instrumented indentation facilities.

New mesoscopic constitutive model for deformation of pearlitic steels up to moderate strains

A new constitutive model for deformation of pearlitic steels has been developed that describes the mechanical behaviour and microstructural evolution of lamellar multi-colony pearlite. The model, a two-phase continuum model, considers the plastic anisotropy of ferrite derived from its lamellar structure but ignores any anisotropy associated with cementite and does not consider the crystal structure of either constituent. The resulting plastic constitutive equation takes into account a dependence on both the pearlitic spacing (arising from the confined slip of dislocations in the lamellae) and on strengthening from the evolving intra-lamellar dislocation density. A Kocks-Mecking strain hardening/recovery model is used for the lamellar ferrite, whereas perfect-plastic behaviour is assumed for cementite. The model naturally captures the microstructural evolution and the internal micro-stresses developed due to the different mechanical behaviour of both phases. The model is also able to describe the lamellar evolution (orientation and interlamellar spacing) with good accuracy. The role of plastic anisotropy in the ferritic phase has also been studied, and the results show that anisotropy has an important impact on both microstructural evolution and strengthening of heavily drawn wires.

Structure and texture of twin roll cast strips of Zn–Cu–Ti zinc alloy

Abstract The structure and crystallographic texture of zinc strips (Zn–Cu–Ti alloy) produced by the continuous horizontal twin roll strip casting method has been characterized. In longitudinal sections normal to the transverse direction, the strips display an approximately symmetrical chevron patterned structure of columnar grains inclined about 30° from the rolling direction. In association with such structure, the macroscopic texture is mainly a ‘normal’ (not cyclic) fibre texture tilted approximately ±30° around the transverse direction plus a similarly tilted weak <0001> fibre texture. A thin layer of small equiaxed grains with a strong (0001) basal texture is present at the free surfaces. The observed structure/texture combination agrees quite well with the expected macrostructure of solidification of the alloy in the twin roll casting process.

Local stress field induced by twinning in a metastable β titanium alloy

A crystal plasticity based finite element model incorporating deformation twinning is applied in 3D to simulate the stress field around a twin lamella in a metastable β titanium alloy. Compared with conventional 2D simulations, the stress field determined by the 3D simulation shows better agreement with that measured experimentally using high resolution electron backscattered diffraction. Reasons leading to the different results in 2D and 3D simulations are discussed. It is also discussed in which circumstances 2D simulation is sufficient, and in which 3D is necessary.