Uniform elongation and the stress-strain flow curve of steels calculated from hardness using empirical correlations

An empirical relationship between the hardness and uniform elongation of non-Austenitic hypoeutectoid steels has been developed. This new hardness-elongation relationship was combined with previously developed correlations of hardness and strength (yield and ultimate tensile strength) to predict the stressstrain flow curve from a single hardness test. The current study considers both power law hardening behavior and exponential hardening behavior. Reasonable agreement was observed between the experimental and predicted flow curves of a high strength, low alloy steel. Additionally, an empirical correlation of the flow strength at instability with hardness is provided. © ASM International.

On the Bauschinger effect in dual phase steel at high levels of strain

The effect of volume fraction and hardness of martensite on the Bauschinger effect in Dual Phase (DP) steel was investigated for strain levels close to those observed in automotive stamping. Five different grades of DP steel were produced by controlled heat treatment allowing the examination of the Bauschinger effect for three different volume fractions of martensite and three levels of martensite hardness. Compression-tension and shear reversal tests were performed to examine the Bauschinger effect at high levels of forming strain. Good correlation between the shear reversal and the compression-tension test was observed suggesting that for DP steel, shear stress strain data, converted to equivalent stress-strain, may be applied directly to characterize kinematic hardening behavior for numerical simulations. Permanent softening was observed following strain reversal and increased with martensite volume fraction and pre-strain level. While the Bauschinger ratio saturates at 3% pre-strain, the Bauschinger strain increases linearly with forming strain without showing saturation. This suggests that to model material behavior accurately in forming processes involving complex loading paths and high levels of strain, test data generated at high strain is required.

Niobium Effects on the Recrystallization Behavior on a Full Austenitic 15Cr-15Ni Stainless Steel Investigated Using Adaptive Neural Networks (ANN)

A new series of austenitic stainless steels-Nb stabilized, without Mo additions, non-susceptible to delta ferrite formation and devoid of intemetallic phases (sigma and chi), without deformation induced martensite is being developed, aiming at high temperature applications as well as for corrosive environments. The base steel composition is a 15Cr-15Ni with normal additions of Nb of 0.5, 1.0 and 2 wt%. Mechanical properties, oxidation and corrosion resistance already have been invetigated in previous papers. In this paper, the effects of Nb on the SFE, strain hardening and recrystallization resistance are evaluated with the help of Adaptive Neural Networks (ANN).

Microstructure-based numerical modeling of the mechanical behavior of Mg alloys

Dentro de los materiales estructurales, el magnesio y sus aleaciones están siendo el foco de una de profunda investigación. Esta investigación está dirigida a comprender la relación existente entre la microestructura de las aleaciones de Mg y su comportamiento mecánico. El objetivo es optimizar las aleaciones actuales de magnesio a partir de su microestructura y diseñar nuevas aleaciones. Sin embargo, el efecto de los factores microestructurales (como la forma, el tamaño, la orientación de los precipitados y la morfología de los granos) en el comportamiento mecánico de estas aleaciones está todavía por descubrir. Para conocer mejor de la relación entre la microestructura y el comportamiento mecánico, es necesaria la combinación de técnicas avanzadas de caracterización experimental como de simulación numérica, a diferentes longitudes de escala. En lo que respecta a las técnicas de simulación numérica, la homogeneización policristalina es una herramienta muy útil para predecir la respuesta macroscópica a partir de la microestructura de un policristal (caracterizada por el tamaño, la forma y la distribución de orientaciones de los granos) y el comportamiento del monocristal. La descripción de la microestructura se lleva a cabo mediante modernas técnicas de caracterización (difracción de rayos X, difracción de electrones retrodispersados, así como con microscopia óptica y electrónica). Sin embargo, el comportamiento del cristal sigue siendo difícil de medir, especialmente en aleaciones de Mg, donde es muy complicado conocer el valor de los parámetros que controlan el comportamiento mecánico de los diferentes modos de deslizamiento y maclado. En la presente tesis se ha desarrollado una estrategia de homogeneización computacional para predecir el comportamiento de aleaciones de magnesio. El comportamiento de los policristales ha sido obtenido mediante la simulación por elementos finitos de un volumen representativo (RVE) de la microestructura, considerando la distribución real de formas y orientaciones de los granos. El comportamiento del cristal se ha simulado mediante un modelo de plasticidad cristalina que tiene en cuenta los diferentes mecanismos físicos de deformación, como el deslizamiento y el maclado. Finalmente, la obtención de los parámetros que controlan el comportamiento del cristal (tensiones críticas resueltas (CRSS) así como las tasas de endurecimiento para todos los modos de maclado y deslizamiento) se ha resuelto mediante la implementación de una metodología de optimización inversa, una de las principales aportaciones originales de este trabajo. La metodología inversa pretende, por medio del algoritmo de optimización de Levenberg-Marquardt, obtener el conjunto de parámetros que definen el comportamiento del monocristal y que mejor ajustan a un conjunto de ensayos macroscópicos independientes. Además de la implementación de la técnica, se han estudiado tanto la objetividad del metodología como la unicidad de la solución en función de la información experimental. La estrategia de optimización inversa se usó inicialmente para obtener el comportamiento cristalino de la aleación AZ31 de Mg, obtenida por laminado. Esta aleación tiene una marcada textura basal y una gran anisotropía plástica. El comportamiento de cada grano incluyó cuatro mecanismos de deformación diferentes: deslizamiento en los planos basal, prismático, piramidal hc+ai, junto con el maclado en tracción. La validez de los parámetros resultantes se validó mediante la capacidad del modelo policristalino para predecir ensayos macroscópicos independientes en diferentes direcciones. En segundo lugar se estudió mediante la misma estrategia, la influencia del contenido de Neodimio (Nd) en las propiedades de una aleación de Mg-Mn-Nd, obtenida por extrusión. Se encontró que la adición de Nd produce una progresiva isotropización del comportamiento macroscópico. El modelo mostró que este incremento de la isotropía macroscópica era debido tanto a la aleatoriedad de la textura inicial como al incremento de la isotropía del comportamiento del cristal, con valores similares de las CRSSs de los diferentes modos de deformación. Finalmente, el modelo se empleó para analizar el efecto de la temperatura en el comportamiento del cristal de la aleación de Mg-Mn-Nd. La introducción en el modelo de los efectos non-Schmid sobre el modo de deslizamiento piramidal hc+ai permitió capturar el comportamiento mecánico a temperaturas superiores a 150_C. Esta es la primera vez, de acuerdo con el conocimiento del autor, que los efectos non-Schmid han sido observados en una aleación de Magnesio. The study of Magnesium and its alloys is a hot research topic in structural materials. In particular, special attention is being paid in understanding the relationship between microstructure and mechanical behavior in order to optimize the current alloy microstructures and guide the design of new alloys. However, the particular effect of several microstructural factors (precipitate shape, size and orientation, grain morphology distribution, etc.) in the mechanical performance of a Mg alloy is still under study. The combination of advanced characterization techniques and modeling at several length scales is necessary to improve the understanding of the relation microstructure and mechanical behavior. Respect to the simulation techniques, polycrystalline homogenization is a very useful tool to predict the macroscopic response from polycrystalline microstructure (grain size, shape and orientation distributions) and crystal behavior. The microstructure description is fully covered with modern characterization techniques (X-ray diffraction, EBSD, optical and electronic microscopy). However, the mechanical behaviour of single crystals is not well-known, especially in Mg alloys where the correct parameterization of the mechanical behavior of the different slip/twin modes is a very difficult task. A computational homogenization framework for predicting the behavior of Magnesium alloys has been developed in this thesis. The polycrystalline behavior was obtained by means of the finite element simulation of a representative volume element (RVE) of the microstructure including the actual grain shape and orientation distributions. The crystal behavior for the grains was accounted for a crystal plasticity model which took into account the physical deformation mechanisms, e.g. slip and twinning. Finally, the problem of the parametrization of the crystal behavior (critical resolved shear stresses (CRSS) and strain hardening rates of all the slip and twinning modes) was obtained by the development of an inverse optimization methodology, one of the main original contributions of this thesis. The inverse methodology aims at finding, by means of the Levenberg-Marquardt optimization algorithm, the set of parameters defining crystal behavior that best fit a set of independent macroscopic tests. The objectivity of the method and the uniqueness of solution as function of the input information has been numerically studied. The inverse optimization strategy was first used to obtain the crystal behavior of a rolled polycrystalline AZ31 Mg alloy that showed a marked basal texture and a strong plastic anisotropy. Four different deformation mechanisms: basal, prismatic and pyramidal hc+ai slip, together with tensile twinning were included to characterize the single crystal behavior. The validity of the resulting parameters was proved by the ability of the polycrystalline model to predict independent macroscopic tests on different directions. Secondly, the influence of Neodymium (Nd) content on an extruded polycrystalline Mg-Mn-Nd alloy was studied using the same homogenization and optimization framework. The effect of Nd addition was a progressive isotropization of the macroscopic behavior. The model showed that this increase in the macroscopic isotropy was due to a randomization of the initial texture and also to an increase of the crystal behavior isotropy (similar values of the CRSSs of the different modes). Finally, the model was used to analyze the effect of temperature on the crystal behaviour of a Mg-Mn-Nd alloy. The introduction in the model of non-Schmid effects on the pyramidal hc+ai slip allowed to capture the inverse strength differential that appeared, between the tension and compression, above 150_C. This is the first time, to the author's knowledge, that non-Schmid effects have been reported for Mg alloys.

Modeling of hardening and softening processes in Mg alloys

The tensile deformation behavior of a range of supersaturated Mg-Al solid solutions and an as-cast magnesium alloy AM60 has been studied. The Mg-Al alloys were tested at room temperature while the alloy AM60 was tested in the temperature range 293-573 K. The differences in the deformation behavior of the alloys is discussed in terms of hardening and softening processes. In order to identify which processes were active, the stress dependence of the strain-hardening coefficient was assessed using Lukac and Balik's model of hardening and softening. The analysis indicates that hardening involves solid solution hardening and interaction with forest dislocations and non-dislocation obstacles such as second phase particles. Cross slip is not a significant recovery process in the temperature range 293-423 K. At temperatures between 473 and 523 K the analysis suggests that softening is controlled by cross slip and climb of dislocations. At temperatures above 523 K softening seems to be controlled by dynamic recrystallisation. (C) 2004 Elsevier B.V. All rights reserved.

Effects of microstructure on the variation of the unloading behavior of DP780 steels

The nonlinear unloading behavior of three different commercial dual-phase steels (DP780 grade equivalent) was examined. These steels exhibited small variations in chemical composition (0.07 to 0.10 mass percent carbon) and martensite volume fraction (0.23 to 0.28), and they demonstrated similar hardening behavior. Uniaxial loading-unloading-loading tests were conducted at room temperature and quasi-static strain rates between engineering strains of 0.5 and 8%. Steel microstructures were examined using electron backscatter diffraction and nanoindentation techniques. The microplastic component of the unloading strain exhibited no dependence on the martensite volume fraction or the ferrite grain size within the small range encountered in this investigations. Instead, the magnitude of the microplastic component of the unloading strain increased as the strength ratio between the martensite and ferrite phases increased. Correspondingly, the apparent unloading modulus, or chord modulus, exhibited a greater reduction for equivalent increments of strain hardening as the strength ratio increased. These results suggest that springback can be reduced in structures containing two ductile phases if the strength ratio between the harder and softer phases is reduced.

Compressive behaviour of nanocrystallilne Mg-5%Al alloys

Magnesium alloys are attracting increasing research interests due to their low density, high specific strength and good mechineability and availability as compared to other structural materials. However, the deformation and failure mechanisms of nanocrystalline Mg alloys have not been well understood. In this work, the deformation behavior of nanocrystalline Mg-5% Al alloys was investigated using compression test, with a focus on the effects of grain size. The average grain size of the Mg-Al alloy was changed from 13 µm to 50 nm via mechanical milling. The results showed that grain size had a significant influence on the yield stress and ductility of the Mg alloys, and the materials exhibited increased strain rate sensitivity with decrease of grain size. The deformation mechanisms were also strongly dependent with the grain sizes.

Evaluation of plastic deformation ability of Cu/Ni/W metallic multilayers

Plastic deformation behavior of Cu/Ni/Wmetallicmultilayers with individual layer thickness ranging from 5 nm to 300 nm is investigated by nanoindentation testing. The experimental results reveal that the composite still exhibits indentation-induced plastic deformation instability and the loss of strain hardening ability at the nanometer scale even if the composite contains two kinds of layer interfaces (face centered cubic(FCC)/FCC and FCC/ body centered cubic) simultaneously. Plastic deformation behavior of the nanolayered material was evaluated and analyzed.

Microstructural evolution and grain boundary sliding in a superplastic magnesium AZ31 alloy

Tensile experiments on a fine-grained single-phase Mg–Zn–Al alloy (AZ31) at 673 K revealed superplastic behavior with an elongation to failure of 475% at 1 × 10−4 s−1 and non-superplastic behavior with an elongation to failure of 160% at 1 × 10−2 s−1; the corresponding strain rate sensitivities under these conditions were 0.5 and 0.2, respectively. Measurements indicated that the grain boundary sliding (GBS) contribution to strain ξ was 30% under non-superplastic conditions; there was also a significant sharpening in texture during such deformation. Under superplastic conditions, ξ was 50% at both low and high elongations of 20% and 120%; the initial texture became more random under such conditions. In non-superplastic conditions, deformation occurred under steady-state conditions without grain growth before significant flow localization whereas, under superplastic conditions, there was grain growth during the early stages of deformation, leading to strain hardening. The grains retained equiaxed shapes under all experimental conditions. Superplastic deformation is attributed to GBS, while non-superplastic deformation is attributed to intragranular dislocation creep with some contribution from GBS. The retention of equiaxed grain shapes during dislocation creep is consistent with a model based on local recovery related to the disturbance of triple junctions.

Three-Dimensional simulation of deformation fields underneath vickers indenter:Effects of power-law Plasticity

The effects of power-law plasticity (yield strength and strain hardening exponent) on the plastic strain distribution underneath a Vickers indenter was systematically investigated by recourse to three-dimensional finite element analysis, motivated by the experimental macro-and micro-indentation on heat-treated Al-Zn-Mg alloy. For meaningful comparison between simulated and experimental results, the experimental heat treatment was carefully designed such that Al alloy achieve similar yield strength with different strain hardening exponent, and vice versa. On the other hand, full 3D simulation of Vickers indentation was conducted to capture subsurface strain distribution. Subtle differences and similarities were discussed based on the strain field shape, size and magnitude for the isolated effect of yield strength and strain hardening exponent.

Effects of temper level on the dependence of fatigue crack growth threshold and crack closure on the prior austenitic grain size

An attempt has been made to systematically investigate the effects of microstructural parameters, such as the prior austenite grain size (PAGS), in influencing the resistance to fatigue crack growth (FCG) in the near-threshold region under three different temper levels in a quenched and tempered high-strength steel. By austenitizing at various temperatures, the PAGS was varied from about 0.7 to 96 μm. The microstructures with these grain sizes were tempered at 200 °C, 400 °C, and 530 °C and tested for fatigue thresholds and crack closure. It has been found that, in general, three different trends in the dependence of both the total threshold stress intensity range, ΔK th , and the intrinsic threshold stress intensity range, ΔK eff, th , on the PAGS are observable. By considering in detail the factors such as cyclic stress-strain behavior, environmental effects on FCG, and embrittlement during tempering, the present observations could be rationalized. The strong dependence of ΔK th and ΔK eff, th on PAGS in microstructures tempered at 530 °C has been primarily attributed to cyclic softening and thereby the strong interaction of the crack tip deformation field with the grain boundary. On the other hand, a less strong dependence of ΔK th and ΔK eff, th on PAGS is suggested to be caused by the cyclic hardening behavior of lightly tempered microstructures occurring in 200 °C temper. In both microstructures, crack closure influenced near-threshold FCG (NTFCG) to a significant extent, and its magnitude was large at large grain sizes. Microstructures tempered at the intermediate temperatures failed to show a systematic variation of ΔKth and ΔKeff, th with PAGS. The mechanisms of intergranular fracture vary between grain sizes in this temper. A transition from “microstructure-sensitive” to “microstructure-insensitive” crack growth has been found to occur when the zone of cyclic deformation at the crack tip becomes more or less equal to PAGS. Detailed observations on fracture morphology and crack paths corroborate the grain size effects on fatigue thresholds and crack closure.

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J(2) flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.

Studies on age-hardening characteristics of ceramic particle/matrix interfaces in Al-Cu-SiCp composites using ultra low-load-dynamic microhardness measurements

Ultra low-load-dynamic microhardness testing facilitates the hardness measurements in a very low volume of the material and thus is suited for characterization of the interfaces in MMC's. This paper details the studies on age-hardening behavior of the interfaces in Al-Cu-5SiC(p) composites characterized using this technique. Results of hardness studies have been further substantiated by TEM observations. In the solution-treated condition, hardness is maximum at the particle/matrix interface and decreases with increasing distance from the interface. This could be attributed to the presence of maximum dislocation density at the interface which decreases with increasing distance from the interface. In the case of composites subjected to high temperature aging, hardening at the interface is found to be faster than the bulk matrix and the aging kinetics becomes progressively slower with increasing distance from the interface. This is attributed to the dislocation density gradient at the interface, leading to enhanced nucleation and growth of precipitates at the interface compared to the bulk matrix. TEM observations reveal that the sizes of the precipitates decrease with increasing distance from the interface and thus confirms the retardation in aging kinetics with increasing distance from the interface.

Effect of strain rate on tensile and compression behaviour of Al-Si/graphite composite

Effects of strain rate (10(-4)-10(-2) s(-1)) on tensile and compressive strength of the Al-Si alloy and Al-Si/graphite composite are investigated. The strain hardening exponent value of the composite was more than that of the alloy for all strain rates during tensile and compressive loading. The yield stress of the composite was more than that of the ultimate tensile strength of the alloy for all strain rates. Tensile and compressive properties of the alloy and composite are dependent on strain rates. The negative strain rate sensitivity was observed for the composite and alloy at lower strain rates during the compression and tension loading respectively. (C) 2011 Elsevier B.V. All rights reserved.

Constitutive Response of Passivated Copper Films: Experiments and Analyses

The constitutive behavior of passivated copper films is studied. Stresses in copper films of thickness ranging from 1000 nm to 40 nm, passivated with silicon oxide on a quartz or silicon substrate, were measured using the curvature method. The thermal cycling spans a temperature range from - 196 to 600°C. It is seen that the strong relaxation at high temperatures normally found in unpassivated films is nonexistent for passivated films. The copper film did not show any rate-dependent effect over a range of heating/cooling rate from 5 to 25°C/min. Further analyses showed that significant strain hardening exists during the course of thermal loading. In particular, the measured stress- temperature response can only be fitted with a kinematic hardening model, if a simple constitutive law within the continuum plasticity framework is to be used. The analytic procedures for extracting the film properties are presented. Implications to stress modeling of copper interconnects in actual devices are discussed.