Recent reports in the literature identified pre-yield stress-strain nonlinearity and hysteresis (anelasticity) as occurring in metals at virtually all stresses. These observations raise foundational questions about metal deformation. Does a critical stress exist below which dislocations are immobile? Is there a critical stress for which permanent deformation occurs? Is anelasticity distinct from elasticity and plasticity? To answer such questions, special tensile tests with loading-unloading cycles after various prestrains were performed for 11 commercial sheet alloys: 9 AHSS (advanced high strength steels) and two Mg alloys. A dissipative dislocation bow-out model of anelasticity was derived that closely reproduces the experimental results and is consistent with the evolving experimental picture of anelasticity. Following prestrain, a finite yield stress was found to exist, below which no permanent deformation or hardening occurs. Anelasticity is distinct from elasticity and plasticity: it is recoverable and dissipative; mechanically reversible and thermodynamically irreversible. Corresponding tests of initial loading suggest radically different conclusions. Without prestrain, i.e. without a developed internal stress pattern, plastic deformation occurs near zero stress. A postulate of local and nonlocal interactions accounting for elastic, plastic and anelastic deformation was proposed.

Shear strain profiles along slip bands in a modified Rolls-Royce nickel superalloy (RR1000) were analyzed for a tensile sample deformed by 2%. The strain increased with distance away from a grain boundary (GB), with maximum shear strain towards the center of the grain, indicating that dislocation nucleation generally occurred in the grain interior. The strain gradients in the neighborhood of the GBs were quantified and generally correlated with rotation about the active slip system line direction. This leads to an ability to determine the active slip system in these regions. The dislocation spacing and pileup stresses were inferred. The dislocation spacing closely follows an Eshelby analytical solution for a single ended pileup of dislocations under an applied stress. The distribution of pileup stress values for GBs of a given misorientation angle follows a log-normal distribution, with no correlation between the pileup stress and the GB misorientation angle. Furthermore, there is no observed correlation between various transmissivity factors and slip band pileup stress. Hence it appears that the obstacle strength of any of the observed GBs is adequate to facilitate the dislocation pileups present in the slip bands. However, slip band transmission does correlate with transmissivity factors, with the current study focusing on the Luster and Morris m’-factor. Observation of strain profiles of transmitted bands indicate dislocation nucleation locations.

A general meso‑scale (GM) crystal plasticity (CP) model was developed that accounts for lower-order (strain hardening) and higher-order (internal stress) effects of geometrically necessary dislocations (GNDs). It is predictive: no arbitrary parameters or length scales were invoked and no ad hoc numerical techniques were employed. It uses general stress field equations for GND content and a novel harmonization technique to enforce consistency of elastic long-range singular defect fields with applied elastic-plastic fields. The model facilitates implementation in commercial finite element programs without requiring special elements, special boundary conditions, or access to element shape functions. GM simulations confirmed, with improved accuracy, previously published predictions of the Hall-Petch effect, Bauschinger effect, and anelasticity. Previously unpredicted phenomena were also predicted: anelasticity and hysteresis for single Ta crystals and strain-hardening stagnation. The internal stresses (higher-order effect) dominate at large length scales, while at small length scales, the GND density hardening (lower-order effect) dominates. GM predicts that strain heterogeneity and consequent GND internal stresses are important factors in anelasticity.

This study explores the evolution of GNDs and their effects on back stress through experimental and computational methods. Four large-grained tantalum tensile specimens were strained in uniaxial tension, electron backscatter diffraction (EBSD) data were collected, and geometrically necessary dislocation (GND) maps of the four specimens in the unloaded state were produced. EBSD-based GND maps revealed several types of features with high GND content which caused back stress in the specimens. Correlations between five geometrically-based grain boundary (GB) transmission factors and the GB GND content were evaluated, and statistically significant correlations were found for transmission factors based on Livingston and Chalmer's N factor, Werner and Prantl's slip transfer number, and GB misorientation. The sign of individual components of the Nye tensor were used to visually and quantitatively identify clustering of GNDs of the same sign, thus giving additional evidence of increasing back stress due to deformation. Deformation of one of the specimens was simulated using multiple CPFEM based modeling approaches and predicted stress-strain responses are compared. The super dislocation model (SD model) — a crystal plasticity finite element method (CPFEM) which incorporates elastic dislocation interactions — was able to isolate impact of back stress on the overall flow stress. The SD model predicted correct stresses when compared with experimental data; however, when the elastic interactions in the SD model were turned off, stress predictions were 25% too low. Thus, demonstrating the importance of incorporating back stress into the model.

Twin boundaries in a crystalline material can be defined by a particular rotation angle about a particular access or a mirrored crystal orientation about a particular plane [1]. For example, copper twins are typically defined by a 60 rotation about where the associated twin plane is of the {111} family. One critical area of twin research looks at deformation twinning as the limiting factor for formability of Mg alloys, such as AZ31 [2]. In AZ31 there are two basic twin modes: compression twinning and tension twinning. The latter phenomenon forms fairly large, easy to detect twinned regions within parent grains, whereas the former tends to form extremely thin twins that are on the order of 100 nm wide. Additionally, the copper which is frequently seen in many microelectronics contains twins on the order of 10 nm [3]. In both cases these features are within the detectable limits for a modern scanning electron microscope (SEM). However, identifying these twins via crystal orientation relations with electron backscatter diffraction (EBSD) in the SEM relies on a larger spatial resolution which makes detecting these twins from crystallographic information difficult in the SEM. This study presents a method whereby improved spatial resolution of thin twins can be achieved with EBSD.

A "bottom-up" representative volume element (RVE) for a dual phase steel was constructed based on measured microstructural properties ("microproperties"). This differs from the common procedure of inferring hypothetical microproperties by fitting to macroscopic behavior using an assumed micro-to-macrolaw. The bottom-up approach allows the assessment of the law itself by comparing RVE-predicted mechanical behavior with independent macroscopic measurements, thus revealing the nature of the controlling micromechanisms. An RVE for DP980 steel was constructed using actual microproperties. Finite element (FE) simulations of elastic-plastic transitions were compared with independent loading-unloading-loading and compression-tension experiments. Constitutive models of three types were utilized: 1) a standard continuum model, 2) a standard Crystal Plasticity (CP) model, and 3) a SuperDislocation (SD) model similar to CP but including the elastic interactions of discrete dislocations. These comparisons led to following conclusions: 1) While a constitutive model that ignores elastic interaction of defects can be fit to macroscopic or microscopic behavior, it cannot represent both accurately, 2) Elastic interactions among dislocations are the predominant source of nonlinearity in the nominally-elastic region (i.e. at stresses below the standard yield stress), and 3) Continuum stress inhomogeneity arising from the hard martensite / soft ferrite microstructure has a minor role in the observed transitional nonlinearity in the absence of discrete dislocation interactions.

Grain boundary dislocation nucleation is simulated in a Nickel bicrystal with Σ21b (211)/(211) grain boundaries. Using molecular dynamics, 386 different triaxial stress states are examined for their effect on dislocation nucleation on different slip systems. The approach leads to dislocation nucleation on six of the twelve partial slip systems, enabling a study of conditions leading to nucleation. The criteria for nucleation on each of the slip systems is shown to have a linear dependence on the resolved shear, normal, and co-slip stresses, though the constants for this linear dependence are unique for each slip system. The combined nucleation criteria are used to construct a theoretical nucleation surface. The surface is reminiscent of a Mohr-Coulomb yield surface, except that in the present case the facets of the surface correspond to nucleation on different slip systems.

Wrought Al-Ge-Si alloys were designed and produced to ensure dislocation bypass strengthening (“hard pin” precipitates) without significant precipitate cutting/shearing (“soft pin” precipitates). These unusual alloys were processed from the melt, solution heat treated and aged. Aging curves at temperatures of 120, 160, 200 and 240°C were established and the corresponding precipitate spacings, sizes, and morphologies were measured using TEM. The role of non-shearable precipitates in determining the magnitude of Bauschinger was revealed using large-strain compression/tension tests. The effect of precipitates on the Bauschinger response was stronger than that of grain boundaries, even for these dilute alloys. The Bauschinger effect increases dramatically from the under-aged to the peak aged condition and remains constant or decreases slowly through over-aging. This is consistent with reported behavior for Al-Cu alloys (maximum effect at peak aging) and for other Al alloys (increasing through over-aging) such as Al-Cu-Li, Al 6111, Al 2524, and Al 6013. The Al-Ge-Si alloy response was simulated with three microstructural models, including a novel SD (SuperDislocation) model, to reveal the origins of the Bauschinger effect in dilute precipitation-hardened / bypass alloys. The dominant mechanism is related to the elastic interaction of polarized dislocation arrays (generalized pile-up or bow-out model) at precipitate obstacles. Such effects are ignored in continuum and crystal plasticity models.

Advanced high strength steels (MISS) pose great challenges to sheet metal forming processes in vehicle components manufacturing with their increasing high strength and surface hardness. Chain-die forming is a recently proposed manufacturing method alternative to roll forming, aiming at reducing the redundant strain by enlarging the deformation length through a remarkably large rotation radius. In this work, the performance of AHSS in chain-die forming is investigated by experiment and simulation. The mechanical tests and chain-die forming tests on four AHSS materials are performed. The Chaboche hardening model to describe the Bauschinger effect of the MISS is established and implemented into the finite element model of chain-die forming process. The evolution of longitudinal strain and springback are elaborated and discussed. Furthermore, a systematic comparison between chain-die forming and roll forming of the U-channel are performed based on the verified FE model. The chain-die forming has obviously smaller and less fluctuate longitudinal strain on the flange, mainly because chain-die forming has a smoother transitional surface. Chain-die forming can alleviate web bow; the flange width of the chain-die formed U-channel presents a monotonic increase trend along the longitudinal direction, while the flange width of the roll-formed shows a fluctuate trend. On the other hand, the springback after chain-die forming is larger than that after roll forming, which implies more compensation is needed to obtain a desired product. (C) 2017 Published by Elsevier Ltd.

Uniaxial stress strain curves are known to exhibit significant curvature and hysteresis even in the nominally elastic regime, i.e. before the standard yield stress is attained. In order to probe the nature of this behavior, hundreds of high -precision loading unloading loading tensile tests were performed using 26 commercial sheet alloys exhibiting a wide range of strength, ductility and crystal structure. Corresponding analysis shows that:1. There is no significant linear elastic region, that is, the proportional limit is O MPa. While the first increment of deformation shows a stress strain slope equal to Young's modulus, progressive deviations of slope start immediately.2. The shape of the transitional stress strain curve can be represented by a simple one -parameter equation representing the "modulus reduction rate." It captures -80% of the measured variation and can be determined from a single test. This approach reduces the error inherent in standard Young's modulus or chord modulus approximations by a factor of 3-6. "3. A "Universal Law" having no independently -determined parameters, i.e. no testing or fitting required, was developed. It captures -90% of the variation represented by the one -parameter representation for the materials tested.The practical and theoretical implications of these results are discussed. On the practical side, the results provide an immediate path to improving applied constitutive models in the transitional regime. An example of an application and results is provided. On the theoretical side, the consistency of the effect for a wide range of metals suggests answers to questions about the governing deformation mechanisms. (C) 2016 Elsevier Ltd. All rights reserved.

Shear fracture can occur when sheet metal is drawn over a tight die radius during forming. Draw-bend fracture (DBF) tests replicate many aspects of the applied forming situation, but not the high strain rates and plane-strain states typical of industrial conditions. In order to improve on the DBF test, a new high-speed, wide, draw-bend fracture (WDBF) test was configured, implemented, and applied to 5 advanced high strength steels (AHSS) with known constitutive behavior and DBF ductility: DP780, DP590, DP980, TRIP780 and TWIP. Finite element (FE) simulations of the WDBF tests were compared with experiments. Similar comparative simulations were carried out for true plane-strain conditions (unattained experimentally) and for standard DBF tests. The WDBF test was found to be better at reproducing industrial conditions than the DBF test over a much wider range of conditions, but even the new configuration remains substantially different from a hypothetical true plane-strain test. The simulations reveal quantitative assessments of the roles of friction, thermo-mechanical deformation and yield surface choice on shear fracture.

Although the initial stress-strain behavior in a tensile test is often characterized as linear elastic up to a yield stress and nonlinear plastic thereafter, the pre-yield transition region is known to exhibit significant curvature and hysteresis. Hundreds of high-precision loading-unloading-loading tensile tests were performed using 26 commercial sheet alloys exhibiting a wide range of strength, ductility and crystal structure. Analysis of the results reveals the following:1. There is no significant linear elastic region; the proportional limit is similar to 0 MPa when measured with sufficient sensitivity.2. Each of the hundreds of measured transitional stress-strain curves can be characterized by a single parameter, here called the "modulus reduction rate." The corresponding equation captures similar to 80% of the observed variation, a factor of 3 to 6 better than a one-parameter linear approximation.3. Most interestingly, the transitional behavior for all alloys follows a "Universal Law" requiring no fit parameters. The law depends only upon the strength of the material and its Young's modulus, both of which are can be measured by independent tests or adopted from handbooks. The Universal Law captures similar to 90% of the variation represented by the one-parameter representation and eliminates the need for mechanical testing to implement and apply.The practical and theoretical implications of these results are discussed. The results provide a simple path to significantly improving applied constitutive models in the transitional regime. The consistency of the effect for such a wide range of metals and suggests that the origin of the behavior lies in the pile-up and relaxation of dislocation arrays.

The literature shows that shear fracture of advanced high strength steels (AHSS) is affected by strain hardening at large strain, as well as the temperature dependence of flow stress and strain hardening. The role of non-isotropic hardening, such as would be expected to be important in reverse strain paths as encountered during draw-bend testing or drawing sheet metal into forming dies, has been difficult to assess without a practical constitutive model combining temperature-dependence and non-isotropic hardening capabilities. Such a model has been developed and implemented in Abaqus Standard via the UMAT subroutine. In order to apply and test the constitutive implementation, the material model was fit using alternate parameter-identification procedures starting from compression-tension (CT) data: 1) fit directly from reverse-path, CT data, and 2) fit indirectly, by combining the direct CT data plus extrapolated data at larger strains where the extrapolation uses verified large-strain monotonic hardening character. The resulting material models were used to simulate draw-bend fracture (DBF) tests for six AHSS. The results show that the indirect method improves the predictions of shear fracture significantly, allowing accurate predictions. It was also shown that the influence of non-isotropic hardening aspects are not critical to accurate predictions as long as the high-strain strain hardening is reproduced accurately. These results suggest a practical and effective method for extending measured tensile hardening to otherwise unattainable strains based on the constant ratio (α in the H/V model) of power-law and saturation-stress strain hardening at a given temperature. The success of this approach suggests that α is a material constant (describing the fundamental strain-hardening character) that depends on temperature but is unaffected by the details of transient hardening following abrupt path changes. Furthermore, the essentially transient nature of hardening following path changes is supported.

Bend-assisted fracture, also commonly called shear fracture, is the splitting of metal sheets during forming in tight-bending regions. It has been shown to be predominantly a result of plastic localization for most advanced high strength steels (AHSS). Such fractures are poorly predicted by typical industrial methods involving finite element modeling (FEM) and forming limit diagrams (FLDs). In order to understand the source of the problem, the sensitivity of simulated shear-fracture formability to material and process parameters was determined using FEM in conjunction with a realistic range of constitutive models, element sizes, and friction coefficients. Two types of shear fracture process were simulated. (1) Draw-bend fracture (DBF) tests are laboratory analogs of industrial forming conditions producing shear fracture; they offer the opportunity of experimental validation but introduce complexity because of varying strain state and unavoidable transitions between shear fracture and tensile fracture. (2) Plane-strain (PS) draw-bend fracture simulations correspond more closely to industrial forming conditions; they simplify the modeling (fixed strain state, no transitions) but no corresponding full-scale laboratory experiments currently exist.The DBF test was found to be sensitive to every material and process parameter tested, with the largest factors being the form of 1-D hardening law and the yield function. Varying these quantities in ranges representing what practical measurements would produce showed variations in predicted formability of up to 80%. The PS simulations, which represent industrial practice more closely, showed large variations in predicted formability only for two variables: 1-D hardening law and friction coefficient. All other parameters were insignificant, except for thermo-mechanical effects, which were important for high-rate tests only.These results show why it is difficult or impossible to predict shear fracture using standard industrial techniques designed for traditional steels. They suggest ways to modify such techniques to accommodate advanced high strength steels. The results also give guidance to alloy designers in terms of which constitutive parameters are most important in inhibiting shear fracture, and which are relatively insignificant. (C) 2015 Elsevier Ltd. All rights reserved.

The mechanically-measured Young’s modulus of metals is consistently lower than the physically measured one, particularly after plastic straining. Furthermore, the nominally elastic loading and unloading behavior is not linear; it shows significant curvature and hysteresis. While many reports of this so-called “modulus effect” have appeared, the consistency of the behavior among grades of steel, or within a single grade produced by alternate methods and suppliers, is unknown. That is, there is little information on whether it is necessary for manufacturers to measure and control the mechanical modulus for every coil of steel in order to guarantee accurate simulations, consistent forming, and reliable in-service behavior. In order to address these issues, 12 steels (4 diverse grades: IF, HSLA, DP600, DP980; 3 producers per grade) were subjected to high-precision modulus measurements using mechanical testing, resonant frequency damping analysis, and ultrasonic pulse-echo techniques. All of these measurements show remarkable consistency among not only suppliers but also among grades. The primary determinant of hysteresis/curvature of the stress–strain response was found to be the nominal flow stress of the alloy. Other variations of overall mechanical modulus are minor compared with hysteresis/curvature. The following conclusions were reached: 1) there is no significant difference among suppliers of a single steel grade, 2) there is very little difference between grades of steel, except for that attributable to differing strengths, 3) mechanical unloading and reloading after pre-strain are similar, 4) cyclic loading and unloading cycles have no accumulated effect except through a minor change of flow stress, and 5) the initial loading or unloading modulus is very similar to the physical modulus, but the mechanically measured slope degrades very rapidly as loading or unloading proceeds, and plateaus at even small strain (<2%). The measured unloading and reloading behavior is more consistent and reproducible than that during initial loading, and unloading behavior is more consistent and reproducible than reloading behavior. Therefore, it is recommended that unloading after pre-strain is used to represent all of nominally elastic nonlinear behavior most accurately.

A practical SuperDislocation Model (SDM) has been developed and implemented to predict dislocation density distributions in a plastically deforming polycrystal and thereby the Hall-Petch effect. The model is composed of two stepwise simulation scales; the first scale is a finite element model of a polycrystal using a novel single-crystal constitutive equation and the second scale redistributes the mobile part of the dislocation density within grains consistent with the plastic strain distribution, and enforces slip transmission criteria at grain boundaries that depend on local grain and boundary properties.In this work, deformation of Fe-3% Si tensile specimen is simulated using SDM to compare dislocation densities obtained from the high-resolution electron backscatter diffraction (HR-EBSD). The model accurately predicts the measured dislocation density at 10% deformation. In addition, size-dependent simulations show that the model qualitatively predicts Hall-Petch slope as well as the grain boundary strength of Fe-3% Si.

•Complex equations include strain hardening, strain-rate sensitivity, and temperature sensitivity.•Reduced starting sets from 28 to 3, an improvement of 8500%.•Uniqueness and accuracy verified for 6 AHSS: DP590/780/980, TRIP780, CP1180, TWIP.•Constitutive equations extrapolate to large, balanced-biaxial strains accurately (up to 6X).•Final equations suitable for predicting shear fracture of AHSS; new form for TWIP.