Deformation Behavior Of Metals Research Articles

Fundamental interaction process between pure edge dislocation and energetically stable grain boundary

The interaction between dislocations and grain boundaries is the principal factor for determining the mechanical properties and the plastic deformation behavior of metals. It is possible to control the grain-boundary microstructure and the macroscopic behavior has been widely exploited for scientific and industrial applications. In atomic scale, however, specific interaction characteristics such as the reaction energy and pathway have yet to be revealed. We have investigated the interaction process between a dislocation and an energetically stable grain boundary, and the quantitative characteristics were determined via atomistic transition state analysis. As a result, the interaction energy is found to be $1.16\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}1}\text{ }\text{eV}/\text{\AA{}}$, which is ${10}^{4}$ times higher than the Peierls potential. The lattice dislocations subsequently experience anomalous dissociations on the grain boundary, which becomes a key factor for the previously unexplained dislocation disappearance and grain-boundary migration.

Hysteresis, Temperature and Resistance Measurements for the Characterization of the Cyclic Deformation Behavior of Metals

Mechanical stress-strain hysteresis, temperature and electrical resistance measurements were performed for the microstructure-related characterization of the fatigue behavior and for the fatigue life calculation of metals. The proceeding fatigue damage was evaluated using the change of the load-free electrical resistance, which is strongly influenced by the defect density of the individual material state. A new test procedure was applied for the fatigue assessment under random loading on the basis of cyclic deformation curves, similar to single step loading. A physically based fatigue life calculation “PHYBAL” was developed, which requires only three fatigue tests for the rapid and nevertheless precise calculation of S-N (Woehler) and fatigue life curves.

Structural states and specific features of the deformation behavior of metals and alloys with mixed nano-and micrograin structure

A classification of the structural states of materials with a mixed nano-and microcrystalline structure is proposed. Theoretical analysis of the structural mechanisms and peculiarities of plastic flow of singlephase and two-phase nanostructured metals and alloys with a bimodal size distribution of grains and phases is performed. The effect of grain-boundary and dislocation mechanisms of plastic flow on the specific features of the deformation behavior and plasticity of nanocrystalline materials is analyzed. A microstructural model of strain hardening of a material with two-scale nano-and micrograin structure is proposed and the condition for the loss of plastic flow stability of such a material is investigated. The dependence of the yield strength and uniform strain of nanocrystalline materials with a two-scale structure on the grain size and the ratio of the volume fractions of the nano-and microstructural components is calculated.

A constitutive equation for the dynamic deformation behavior of polymers

A constitutive equation based on the generalized concept of thermally activated flow units is developed to describe the stress–strain behavior of polymers as a function of temperature, strain-rate, and superposed hydrostatic pressure under conditions in which creep and long-term relaxation effects are negligible. The equation is shown to describe the principal features of the dynamic stress–strain behavior of polytetrafluoroethylene and, also, the yield stress of polymethylmethacrylate as a function of temperature and strain rate. A key feature of the model, not utilized in previous constitutive equation descriptions, is an inverse shear stress dependence of the shear activation volume. In contrast to metal deformation behavior, an enhanced strain hardening with increasing strain at higher strain rates and pressures is accounted for by an additional rate for immobilization of flow units. The influence of hydrostatic pressure enters through a pressure activation volume and also through the flow unit immobilization term. The thermal activation model is combined with a temperature dependent Maxwell–Weichert linear viscoelastic model that describes the initial small strain part of the stress strain curve.

Chemical Complexity in Mechanical Deformation of Metals

Prediction of the deformation behavior of metals in the presence of environmentally embrittling species like water or hydrogen, or under presence of organic reactive chemicals, remains a critical challenge in materials modeling. Here we propose a combination of the first principles-based reactive force field ReaxFF and the embedded atom method (EAM) in a generic multi-scale modeling framework, the Computational Materials Design Facility (CMDF), that enables the treatment of large reactive metallic systems within a classical molecular dynamics framework. Our hybrid method is based on coupling multiple Hamiltonians by weighting functions, which allows accurate modeling of chemically active sites with the reactive force field, while other parts of the system are described with the computationally less expensive EAM potential. We apply our hybrid modeling scheme in a study of fracture of a nickel single crystal under the presence of oxygen molecules. We observe that the oxide formed on the crack surface produces numerous defects surrounding the crack, including dislocations, grain boundaries, and point defects. We show that the mode of crack propagation changes from brittle crack opening at the crack tip to void formation ahead of the crack and void coalescence for lll orientation of the crack. Our results illustrate the significance of considering oxidative processes in studying deformation of metals, an aspect largely neglected in most modeling work carried out with pure EAM potentials. Our hybrid method constitutes an alternative to existing methods that are based on coupling quantum mechanical methods, such as density functional theory, to empirical potentials.

Structure−Property Correlations in Bending and Brittle Organic Crystals

Bending of crystals of molecular solids occurs when the strength of intermolecular interactions in orthogonal directions is significantly different. We report here a survey of 60 molecular crystals and establish a causative correlation between bending and crystal packing. This group contains crystals with 4 and 8 Å crystal axes and includes 1D, 2D, 3D, isostructural, polymorphic, stacked, interlocked, single, and multicomponent crystals and solvates. We found that 17 of these 60 crystals may be bent, whereas the rest are brittle and cannot be bent plastically. The bending crystals could be deformed into many shapes; sometimes, they could even be flattened upon themselves without breakage. A model for bending is proposed using the information obtained from X-ray diffraction, face indexing, and mechanical property measurements on both bending and non-bending (brittle) crystals. The bending and brittleness of these molecular crystals are discussed in comparison with the deformation behavior of metals. Molecular crystals show practically no change in volume and the lengths of the inner and the outer arcs and the sample thickness are unchanged following plastic bending. This is in contrast with the bending of metallic materials, in which a decrease in thickness is evident. Isotropic crystals with comparable intermolecular interactions in the three orthogonal directions are “cross-linked” and do not bend; they are hard and brittle. Mechanical properties of molecular crystals are important because they vary with the crystal form and have major implications for large-scale processing and handling of materials in industry, especially the pharmaceutical industry.

A dislocation density based strain gradient model

Strain gradients play a vital role in the prediction of size-effects in the deformation behavior of metals at the micrometer scale. At this scale the behavior of metals strongly depends on the dislocation distribution. In this paper, a dislocation density based strain gradient model is developed aiming at predictions of size-effects for structural components at this scale. For this model, the characteristic length is identified as the average distance of dislocation motion, which is deformation dependant and can be determined experimentally. The response of the model is compared to the strain gradient plasticity model of Huang et al. [Huang, Y., Qu, S., Hwang, K.C., Li, M., Gao, H., 2004. A conventional theory of mechanism-based strain gradient plasticity. Int. J. Plasticity 20, 753–782]. It is shown that the present strain gradient model, which only requires a physically measurable length-scale, can successfully predict size effects for a bar with an applied body force and for void growth.

라체팅 거동에 대한 점소성 구성방정식

Inelastic deformation behavior of metals and alloys is considered rate dependent. Uniaxial ratcheting experiments performed by Ruggles and Krempl, and Hassan and Kyriakides exhibited that higher mean stress for a fixed stress amplitude resulted in higher ratchet strain within a rate independent framework and higher stress rate resulted in lower ratchet strain, respectively. These phenomena are qualitatively investigated by numerical experiments through unified viscoplasticity theory. The theory does not separate rate-independent plasticity and rate-dependent creep, and thus uses only one inelastic strain to describe inelastic deformation processes with the concept of the yield surface. The growth law for the kinematic stress, which is a tensor valued state variable of the constitutive equations, is modified to predict the linear evolution of long-term ratchet strain.

Effects of chamber shapes of porthole die on elastic deformation and extrusion process in condenser tube extrusion

Abstract This paper describes a 3D FEM simulation of porthole die extrusion process for producing condenser tubes used for a cooling system of automobiles. In general, condenser tube is mainly manufactured by the conform extrusion method, but this process is less effective as compared with the direct extrusion method in productivity per unit time and in the equipment investment. Therefore, it is essential for the conversion to the direct extrusion with porthole die that can produce condenser tube with competitiveness in costs and qualities compared with the existing conform extrusion. However, an experimental method to quantify the deformation behavior of porthole die for condenser tube extrusion has not been established yet, due to its complicated die assembly and complexity of metal flow. FEM is a good alternative to evaluate the three-dimensional deformation behavior of metals in condenser tube extrusion. Especially, an understanding of metal flow in porthole die extrusion is important, because it provides necessary information in die design for high performance extrusion. This study was designed to evaluate material flow, welding pressure, extrusion load, and the tendency of mandrel deflection that is affected by variation of chamber shape on porthole die. An estimation was carried out using FE analysis in non-steady state. Also, this study examined into the mandrel fracture behavior through investigating elastic deformation of mandrel during the extrusion.

Rate (time)-dependent deformation behavior: an overview of some properties of metals and solid polymers

The inelastic deformation behaviors of metals and polymers are discussed with the aim of finding a common base that would simplify academic and engineering analyses. Only monotonic loading conditions at room temperature are considered. For loading at different rates, nonlinear relations between loading rate and stress level, creep stress level and creep strain, and relaxation rate and stress were common to both type of materials. There are, of course, significant differences in elastic properties, strength levels and the strains involved. Special properties such as relaxation behaviors and creep anomalies can be qualitatively and quantitatively reproduced by the state variable model VBO (viscoplasticity theory based on overstress). Since experimental investigations typically concentrate on one particular aspect of inelastic deformation behavior such as creep or strain-rate dependence, it is often difficult to gather a comprehensive data set for a given material. In spite of this, considerable similitude in the deformation behavior of metals and polymers in various test conditions has nevertheless been established.

Finite element analysis of deformation behaviour of metals during equal channel multi-angular pressing

In the present paper, the plastic deformation behaviour of materials during equal channel multi-angular pressing (ECMAP) of routes A and C, with a theoretical total strain of ≈2 upon a single pass, was studied using the two dimensional rigid-plastic finite element method. The ECMAP process is described in terms of the two stages based on the die filling procedure. Numerical simulation for annealed pure copper showed that the first corner gap that occurred during stage I was not formed during stage II owing to the back pressure developed due to the second intersection deformation. The back pressure effect results in the local severe shear at the bottom of the ECMAP sample for the processing routes A and C. While the overall shear deformation is more intensive in the route A sample and is lessened in the reverse direction in the route C sample due to the difference in the shear direction of the first and the second shear, the effective strain along the width direction for the route A processed workpiece is more homogeneous than that of the route C processed workpiece. The results suggest the possibility of obtaining homogeneous deformation resulting in isotropic samples by controlling the deforming route.

Torsion and bending of micron-scaled structures

Typical microelectromechanical systems (MEMS) devices and packages are composed of micron-scaled structures. Experimental investigations on the effect of size on the deformation behavior of simple structures have shown that the deformation behavior of metals and polymers is size dependent. The size dependence in small structures is attributed to the contribution of nonnegligible strain gradients. In this work, torsion and bending of micron-sized rods and plates were analyzed by using a two-parameter model of strain-gradient plasticity. Microrod torsion and microplate bending experimental data were analyzed to determine the magnitude of the strain-gradient material parameters. The parametric analyses showed that conventional analysis is applicable only when the size of the structure is significantly larger than the material parameters, which are typically in the micron range. Strain-gradient analysis of micron-sized rod revealed that the presence of strain gradient increased the torque by three to nine times at the same twist. For MEMS structures with micron-sized features, conventional structural analysis without strain gradient is potentially inadequate, and strain-gradient analysis must be conducted to determine the elastoplastic behavior in the micron scale.

Influence of the microstructure on the deformation behaviour of metal–matrix composites

In this contribution, investigations of the influence of the microstructure on the macro-, meso- and micro-effects in metal–matrix composites are presented by direct combination of experiment and simulation. The aim of the presented work consists in an improved understanding of the mechanical behaviour of heterogeneous materials by combining information of different length scales.

Deformation mechanism maps for polycrystalline metallic multiplayers

Metallic multilayers represent an ideal vehicle for the exploration of length scales in plasticity. They also provide the opportunity to synthesize materials with controlled interfaces and structures for the production of materials close to the theoretical strength. In the present investigation, the authors present a simple analysis that allows us to obtain limiting values of microstructural scales at which these different mechanisms operate. They present the results in the form of two-dimensional maps of layer thickness and grain size ranges over which different deformation mechanisms operate. These maps are intended to be guidelines for interpreting the scale-dependent strengthening or softening mechanisms in multilayers, in the same manner as Ashby's deformation mechanism maps for temperature and stress dependent deformation behavior of metals. An attempt to extend Ashby's deformation mechanism maps to Al thin films by Frost revealed that the predicted strain rates were several orders of magnitude higher than the observed rates due to the higher flow stresses of thin films. Hence, more work is needed to incorporate the fundamental differences in the deformation behavior of thin films and bulk polycrystals to map the mechanisms as a function of stress, temperature and microstructural scale. In this article the authors only considermore » changes in deformation mechanisms with decreasing length scales at constant temperature and strain rates.« less

Multiscale Polycrystal Plasticity

Polycrystal plasticity models are commonly developed with a narrow focus on the grain as the fundamental unit of crystallographic orientation and anisotropic behavior. However, deformation and strengthening mechanisms occur simultaneously at multiple length scales and may lead to bulk deformation behavior of metals that is substantially different from that predicted by simple forms of polycrystal plasticity. The development of dislocation substructure occurs at subgrain scales while, at the same time, geometrically necessary dislocation boundaries (GNBs) are generated that extend over several grain diameters. A framework is presented here for the efficient treatment of multiple, simultaneously evolving strengthening mechanisms. The theory focuses on a macroscale hardening surface representation of the strengthening due to GNB formation. Crystallographic shear flow resistance is determined via a mapping procedure of the macroscale hardening surface to the length scale of grains. Predicted stress-strain curves based on the hardening surface formulation are compared to experimental data and polycrystal plasticity predictions for OFHC Cu. It is demonstrated that the hardening surface model of GNB strengthening mechanisms can provide improved predictive capability of nonproportional loading behavior of Cu compared to conventional slip system hardening laws commonly used in polycrystal plasticity applications.

A crystallographic model for the study of local deformation processes in polycrystals

Abstract Most engineering materials possess a polycrystalline structure. Under load the anisotropy of the constituent grains leads to strong inhomogeneities of stresses and strains on the grain level. In order to investigate the local deformation processes, a new crystallographic model for pure fcc metals in the low temperature range has been developed. It is based on the framework of crystal plasticity and uses the finite element method (FEM). The rate dependent constitutive equations consider isotropic as well as kinematic hardening, whereby the mutual interactions of dislocation processes on the different slip systems are taken into account. Comprehensive calculations show that the essential features of both single crystals—which serve as a test object for the constitutive equations—and polycrystals are reproduced correctly. Moreover the simulations allow a deeper understanding of the mechanisms that control the local deformation behaviour of metals, especially of the mutual interactions of slip system activity, local hardening and resulting local strain. Furthermore, the model may serve as a physically motivated base for a later inclusion of damage terms which allow investigations of damage and fatigue on the local scale.

Nanohardness measurements for studying local mechanical properties of metals

Studying local mechanical properties of metallic alloys and composites and their defect structures such as grain boundaries, cracks, and dislocations allows a better understanding and design of these structural materials. With a nanoindenting atomic force microscope (NI-AFM), which uses diamond tips, such measurements are possible on a nanometer scale. Measurements on the microstructure of superalloys are presented, where different precipitates with sizes in the range of 100 nm are characterized by their different hardness values. In addition, this new technique was used to characterize the nanohardness of the plastic zone and stress fields of cracks and grain boundaries. Therefore, crack tips of in-situ loaded bending specimens of intermetallic alloys (NiAl) were investigated. The measurements show a change in nanohardness and elasticity from the distance of interfaces. In material science the high-resolution capabilities of the atomic force microscopy (AFM) are used for studying metallographic sections, where different phases produce topographic contrasts in the image. A extremly small height difference in the microstructure is sufficient for a height contrast in the image, which allows a quantitative determination of particle size distributions and volume contents of precipitates [1, 2]. The plastic deformation behavior of metals is strongly influenced by the distribution and movement of defects as dislocations, grain boundaries and cracks. In-situ loading experiments in an AFM on specimens loaded in 4-point bending demonstrate the good imaging properties of an AFM for such defects [3]. Mechanical properties such as Young’s modulus of elasticity and hardness values were obtainable in the past by various indentation techniques, where a load displacement curve is recorded during the indentation process. These techniques were mainly applied for studying the mechanical properties of thin films. A combination of a nanoindenting instrument with an AFM now allows the local mechanical properties of different phases and particles in metallic alloys to be measured, since the indents can be positioned very exactly with the AFM. Such a combined nanoindenting AFM (NI-AFM) requires a special force measurement technique. Piezo hysteresis and creep of the used piezo scanner have to be eliminated. In addition, indenting should be performed by a tip which is centrally fixed and not at the end of a bending beam (cantilever) [4], because otherwise the location of the indent changes during loading. These properties are fulfilled by a capacitive transducer, which is used for load generation and measurement instead of the standard laser deflection unit. A diamond tip is used for the indentation experiments and topographic imaging in a conventional AFM mode. The resulting force indentation curves contain two pieces of information: the universal hardness H and the reduced modulus of elasticity Er. The possibilities of the NI-AFM for studying local mechanical properties are demonstrated on two different examples: first the hardness of the superalloy CMSX-6 was characterized; second, local changes of mechanical properties near a crack tip in a NiAl single crystal were examined. 1 Experimental setup and sample preparation The nanoindentation measurements shown in this paper were performed with an add-on-force transducer from Hysitron Inc. This transducer, mounted on a conventional AFM, controls the z movement of the tip (indentation, applied load, and feedback signal) while the piezos of the AFM control the lateral x-y movement. Further technical details on the transducer are described in [5]. Specimens of the superalloy CMSX-6 were examined with a Nanoscope II AFM from Digital Instruments. Since the x-y movement is achieved by scanning the whole specimen, only small specimens with a maximum diameter of 20 mm can be analyzed. Crack tips in NiAl single crystals were investigated with a bending apparatus specially constructed for the Explorer AFM from TopoMetrix. (This bending apparatus is described in [6].) Because the whole transducer assembly is mounted on the x-y scanner, the combined system is more sensitive to mechanical noise. However, large specimens can be examined with

Constitutive equations for modelling flow softening due to dynamic recovery and heat generation during plastic deformation

The flow softening of metals at elevated temperatures is modelled in this paper based on the theory of viscoplasticity. A single internal state variable constitutive model is presented to represent the deformation behavior of metals that exhibit flow softening caused by the competing hardening and recovery processes and heat generation during plastic deformation. The constitutive equations are validated by hot torsion testing that has advantage over tension and compression in generating flow stress to large strains. The material constants determination methods have been developed and successfully applied to aluminium alloy 5083 over a wide range of strain rates and temperatures. The prediction of the flow stress in aluminium alloy 5083 as a function of strain rate, temperature and strain has shown to be in good agreement with the test data.

Cyclic deformation behavior of a co-axial symmetrical copper bicrystal

Bicrystals are widely used to demonstrate the grain boundary (GB) effects on plastic deformation behavior of metals and alloys. In a series of reports to be followed the authors will investigate the effect of the slip continuity across GB, the strain incompatibility at GB and the interaction of dislocation with GB on the cyclic deformation behavior by using different type of copper bicrystals. In the present report, the cyclic deformation behavior of a co-axial symmetrical bicrystal of which the component crystals are single-slip-oriented was investigated.

The experimental simulation of deformation behavior of metals in the conform process

In this paper, the deformation behavior of the conform continuous extrusion forming) process has been studied by experimental simulation. In the experimental arrangement, the frictional force can be taken as the driving force that effects the plastic deformation of the metal through the die. A Moiré method is utilized for investigating the plastic flow of the metal in the experimental simulation. It is found that an intense internal shear band (IISB) exists in the plastic deformation zone. The existence of the IISB can not only mitigate the inhomogeneity of plastic deformation, but can also improve the attainable level of plastic deformation of the metal.