Plastic Behavior Of Metals Research Articles

Plastic Behavior of Metals and Their Sensitivity to Grain Size: Comparison between Two Multiscale Approaches

This study evaluates two multiscale models to determine their ability to describe the effect of grain size (GS) on the plastic behavior of ultrafine-grained (UFG) and nanocrystalline (NC) materials. One model follows the Hall–Petch type (Model-1), while the other adopts dislocation kinematics to illustrate the grain boundary effect (Model-2). The stress–strain relation was utilized to present predictions about how various copper and nickel grain sizes affect the evolution of their plastic behavior. These predictions were compared to each other and their respective experimental databases. The copper databases stem from a well-known published paper, while the nickel databases were sourced from a research project. An analysis was conducted to evaluate each model’s ability to replicate the critical value (dcrit) for the UFG to NC transition. In the case of copper, both models produce a comparable dcrit of 16 nm. Model-1 has a lower sensitivity to yield stress below this value compared to Model-2. Both models accurately describe the weakening phase of metals below dcrit, particularly Model-2. The maximum error of 11% for copper was observed in Model-1, whereas Model-2 predicted a minimum error of 0.6%.

A new concept for continuum distortional plasticity

This paper presents hexah, a framework based on the homogeneous anisotropic hardening (HAH) model. It aims at recreating the effects of arbitrary strain path changes over the plastic behavior of metals. Its core relies on the concept of microstructure deviator, a tensor representing one set of active slip systems. The present theory makes use of an arbitrary number of microstructure deviators spawned by abrupt changes of loading paths. A formalism is detailed to describe a smooth evolution from one set of activated slip systems to another. This new approach carries significant advantages: evolution equations are simplified, the number of parameters decreased, and the behavior near cross-loading stabilized.

Material length scale of strain gradient plasticity: A physical interpretation

The physical basis and the magnitude of the material length scale in theories of strain gradient plasticity are crucial for accounting for size effects in the plastic behavior of metals at small scales. However, the underlying physics of the length scale is ambiguous. The length scales in strain gradient plasticity theories in which the plastic work density can be expressed as a function of the gradient-enhanced plastic strain are here derived from known physical quantities via critical thickness theory. A connection between the length scale and the fundamental physical quantities is elucidated. The combination of the strain and strain-gradient terms within the deformation theory of strain gradient plasticity is addressed. It is shown that, compared with the harmonic sum of the strain and strain-gradient terms in Fleck-Hutchinson theory, the linear combination gives a more reasonable value of length scale, several micrometers, which is close to that in the gradient theory of Aifantis. In contrast, the value of length scale in Nix-Gao theory is much larger, in the millimeter range. The length scales determined by critical thickness theory are in good agreement with those obtained by fitting to experimental data of wire torsion.

Parameter Estimation of Metal Plasticity from Time History Data of Taylor Impact Test

Characterisation of material response under intensive dynamic loading due to explosion or projectile impact bears great importance as material properties are significantly influenced by strain rate. Among the several available methods, Taylor impact test is the simplest experimental approach for characterizing plastic behaviour of metals under high strain rate (up to 105 s-1). Here in, a cylindrical rod is impacted upon a rigid stationary anvil and the dynamic yield strength is estimated from the final deformed dimensions of the rod. Development of high speed photography enables the capturing of the time evolution of these dimensions experimentally. These time histories are rich with information about the material plastic behaviour and thus using them in estimating metal plasticity would be an important development. In the present study, an attempt is made to formulate an inverse problem and estimate parameters of metal plasticity using the time history data obtained from the Taylor impact test.

The Contribution of History in Plastic Behavior of Metals in Machining

Mechanical and thermal properties significantly affect many aspects of machining, such as chip formation, cutting forces, cutting temperatures, and surface integrity of machined products. One of the most important mechanical properties is the material flow stress, which is governed by the field variables including the strain, strain rate, and temperature. Due to the presence of high values of these variables in machining, it is important to evaluate the performance of different material models, typically developed at much lower strains, strain rates, and temperatures. The other issue is to identify the effect of the history of these variables that material microvolume experiences while moving through the shear zones and include them in the model. It is demonstrated that such material models may be suitable choices to describe the material flow in simulation of machining, which leads to an extrapolation from the mathematical form of these models. In addition, this paper discuses the importance of history dependency in flow stress and compares the performance of three commonly employed material constitutive models including the nonhistory-dependent Johnson–Cook (J–C) model, the empirical Oxley model, and the history-dependent Maekawa model. It is demonstrated that among the metals with different crystal structures, the flow stress of face-centered cubic (FCC) metals is highly affected by the strain path and is very little sensitive to temperature and strain-rate changes. In addition, the magnitudes of these effects are discussed.

Increase of bending strength and maximum deflection of concrete reinforced with CFRP strips

AbstractIn 1981, many detached houses collapsed owing to the earthquake which took place at the coast of Miyagi Prefecture in Japan, because ferroconcrete was not used as the base of most of the collapsed houses. Therefore, the earthquake-proof design criterion was revised and it was obliged to use ferroconcrete as the base of detached houses ever since. However, there are still more than 10 million detached houses using aged concrete as the base in Japan. In this paper, a reinforcement method for the aged concrete is demonstrated by using the high performance carbon fiber reinforced plastic (CFRP) strips. Three kinds of concrete beams reinforced with the CFRP strips with different vertical insert positions and different numbers of the CFRP strips were tested by a four point bending test method. In order to clarify the effects of CFRP strips, a concrete beam without reinforcement was also tested. The results of the experiment showed that the maximum deflections of the concrete beams reinforced with the CFRP strip were more than 100 times larger than those of the concrete beams without reinforcement. Although the concrete beams without the CFRP strips collapsed instantly, the concrete beams reinforced with the CFRP strips gradually failed, which were similar to the plastic behavior of metals. This result means that the residents can afford to escape safely from the houses in the event of possible earthquakes. The experimental results were compared with the analytical ones obtained from the composite beam theory and the failure criterion. Both results showed good agreement and the effectiveness of base concrete reinforced with CFRP strips was demonstrated.

Plasticity model for metals under cyclic large-strain loading

This paper deals with mathematical modeling of one of the effective technologies of plastic metal forming — multistep cold metal forging. Experimental results are given on the plastic behavior of metals under cyclic loading at large strains accumulated for one cycle. Based on the experimental data obtained, a plasticity model is developed and shown to be effective in testing and improving the technology of forging a nut blank by using a computer-aided engineering analysis system.

Editorial

This special issue of the Journal of Engineering Materials and Technology (JEMT) contains selected papers from the first symposium organized on shear; SHEAR07 in Nancy, France, 4–7 September, 2007. All papers have successfully gone through the regular peer-review process of JEMT.Shear deformation is one of the basic deformation modes in testing and metal forming. It usually permits to reach much larger strains than in other deformation modes. The main objective of this issue is to provide an insight into the large variety of topics that are related to shear and to publish new advances in testing, material behavior and modelling.Although the selected papers cannot cover all topics related to shear, the present collection represents a good discussion about effects related to large strain shear (torsion), hardening behavior, adiabatic shear bands at high strain rates, specific rules for dynamic recrystallization in shear, advanced crystal plasticity analyses, texture development and testing of polymers. One can present the essential of the contributions as follows:After an analysis of the shear process and grain refinement in Equal Channel Angular Extrusion, the paper entitled “Plastic Behavior of Metals at Large Strains: Experimental Studies Involving Simple Shear” presents a new model on Stage IV strain hardening.There are two papers on high strain torsion of an intermetallic alloy, the NiAl: “Texture Formation and Swift Effect in High Strain Torsion of NiAl” and “Microstructure Development During High Strain Torsion of NiAl.” They present original experimental data on texture and microstructure at large strains and varying temperatures together with good simulation results concerning the Swift effect. The latter is always important in free-end torsion and is shown to be related to the evolution of the crystallographic texture.The contribution entitled “Analysis of Large Strain Hot Torsion Textures Associated With ‘Continuous’ Dynamic Recrystallization” presents new principles and successful modelling for the dynamic recrystallization process that changes the texture at higher temperatures during shear.The torsion of non-axisymmetric initial textures is analyzed in the paper “Texture and Mechanical Behavior of Magnesium During Free-End Torsion” including polycrystal plasticity modelling of the texture development and new ideas about dynamic recrystallization in hexagonal materials.There are two theoretical papers that give insight into the shear process in metal forming and the selection of slip systems: “Identification of Simple Shear in Plane Strain Deformation” and “Shear on the Flow Surface of Metallic Crystals.”A complex shock-related problem is addressed in the paper “Numerical Study of Impact Penetration Shearing Employing Finite Strain Viscoplasticity Model Incorporating Adiabatic Shear Banding” for the case of dynamic plasticity of high-strength metallic materials.The hardening characteristics of polymers strongly depends on the crystalline phase which deforms mainly by simple shear as shown in the paper “Determination of Critical Strains in Isotactic Polypropylene by Cyclic Loading-Unloading.”Finally, I thank gratefully all the authors for their excellent contributions to this special issue and the Editors of JEMT, Professors Hussein Zbib and Huseyin Sehitoglu for giving the opportunity to publish the most relevant contributions of the SHEAR07 symposium. Special thanks to Professor Christian GSell, the Chairman of SHEAR07 for bringing the scientific community together on shear processes and related phenomena.

Plastic Behavior of Metals in Reverse Straining after Large Pre-Strains

The present work examines the reversal response of a face-centered cubic (fcc) polycrystalline metal after large pre-strains. While reversal responses among different fcc metals are similar after small pre-strains, they can vary widely after large pre-strains depending on material and microstructure. In this article, these characteristics are considered to be governed by three distinct mechanisms: (1) reverse glide of dislocations previously held by backstresses, (2) reverse glide of dislocations previously held by barriers, and (3) ‘reverse hardening’ by reverse glide over stable dislocation barriers formed in pre-straining. These small-scale mechanisms are incorporated into a polycrystal code to investigate their influence on the macroscopic reversal response and to interpret large strain reversal tests in the literature. It is shown that mechanism (2) is responsible for worksoftening and reductions in hardening rate and mechanism (3) for the overshoot seen in α- brass and other low stacking fault energy alloys. Mechanism (1) is responsible for the Bauschinger effect and occurs in all metals. A large fraction of second phases leads to a strong Bauschinger effect that can either reduce or postpone the effects of mechanisms (2) and (3).

New constitutive equation for plasticity in high speed torsion tests of metals

Present work investigates a phenomenological plasticity equation for the plastic behavior of metals deformed in high speed torsion tests. The tests were carried out at room temperature in a laboratory torsion test equipment and also in an universal tensile test machine on annealed commercial pure copper and aluminum specimens. The tensile tests were performed at room temperature by an universal testing machine at low strain rate of 0.017/s. The experimental torsion tests were carried out at constant angular speed that imposed a constant shear strain rate to the specimen. In the tests, the rotation speed were set to 61 rpm and 200 rpm which imposed high strain rates of about 2/s and 6.5/s respectively in tubular specimens. The torsion test lasted between 0.5 s and 1 s. The experimental hardening curves of equivalent stress versus strain in torsion were sigmoidal type and were fitted by different constitutive equations for plasticity that takes into account the strain hardening and thermal softening effects due to local temperature increase as the Johnson-Cook model, the modified Voce equation and others. The specimen local temperature increase was calculated assuming adiabatic deformation process. It is proposed a new constitutive equation or modified Voce equation for the equivalent flow stress which considers the effects of strain hardening, strain rate hardening and thermal softening for the best fit to the present experimental data of annealed aluminum and copper.

Modeling of processes of complex plastic deformation of materials along arbitrary temperature and force loading paths

We develop a mathematical model describing the processes of complex plastic deformation of structural materials (metals and their alloys) under multiaxial nonproportional paths of complex temperature and force loading. To obtain qualitative and quantitative assessment of the constitutive relations developed here, we study how the strain path shape affects the plastic behavior of metals. We show that the version of constitutive relations developed here correctly represents the main elastoplastic deformation effects in metals for arbitrary strain paths.

An endochronic model of material function and its application to plastic behavior of metals under asymmetric cyclic loadings

By using the incremental form of the endochronic theory of plasticity, a model of material function is proposed in this paper to investigate plastic behavior. By comparing the stress-strain hysteresis loop, the theory is shown to agree well with the experimental results, especially in the evolution of peak stress values of SAE 4340 steel loaded by cyclic loading with various amplitudes. Depending on the choice of material parameters, the present model can substantially result in six categories of material function, each of which can behave differently with respect to an identical deformation history. In addition, the present model of material function is shown to be capable of describing the behavior of erasure of memory of materials, as experimentally observed by Lamba and Sidebottom (1978).

The mean free path of dislocations in nanoparticle and nanorod reinforced metal composites and implication for strengthening mechanisms

The mean free path length of dislocations plays an important role in the plastic behavior of metals, which may be significantly enhanced by the addition of nanoparticles. The effects of particle distribution pattern, particle size, shape and volume fraction on the dislocation mean free path length and average obstacle distance are analyzed in two- and three-dimensional models. As the particle volume fraction increases, the dislocation mean free path length and average distance between dislocations obstacles can be significantly reduced, implying enhancement of strength. The random particle distribution exhibits the best combination of dislocation mean free path length and average obstacle distance. In addition, both dislocation mean free path and average obstacle distance can be significantly reduced by changing the particle shape from nanosphere to nanorod. The present analysis may provide useful information for designing the particle enforced composite materials.

Convex fourth and sixth-order plastic potentials derived from crystallographic texture

The anisotropic plastic behaviour of metals (without prestrain) can be described rather accurately by means of polycrystalline deformation models based on the Taylor theory. This crystallographic anisotropy can be incorporated into finite-element simulations by means of a semi-analytical approach, using plastic potentials of which the coefficients are derived from the Taylor model and the texture. The convexity of the adopted expressions has since long been a problematic issue. In this paper a new class of potential functions in strain-rate space is introduced. These have the advantage that convexity can be strictly imposed. The new formulation is critically assessed for a bcc material with a sharp model texture consisting of a Gaussian distribution centered around the (100)[011] orientation and with a spread of 11 degrees.

Anisotropic plastic potentials for polycrystals and application to the design of optimum blank shapes in sheet forming

Recently, some potentials were proposed to analytically describe the plastic behavior of orthotropic metals. These potentials, when expressed in six-dimensional stress space, were called yield functions or, when expressed in six-dimensional strain-rate space, were called strain-rate potentials. It was shown that these phenomenological potentials provide good approximations of the plastic potentials calculated with polycrystal models. They can be used for any type of loading condition, and they can account for orthotropic anisotropy. In a parallel effort, called ideal forming theory, a forming design theory that optimizes processes and initial blank shapes in sheet forming was developed. This ideal forming theory was implemented in a finite element modeling code in order to design the blank shape directly from the final part shape. The main input to this model includes the final part geometry and the constitutive behavior of the material. In the present article, the constitutive equations describing the plastic behavior of metals as well as the main features of the ideal forming theory are briefly summarized. Then, application of the strain-rate potential to the design of a blank shape for a circular cup drawn from an anisotropic Al-Li sheet is presented. It is shown that the design code efficiently predicts the shape of the blank needed to obtain a cup with minimal earing from a highly anisotropic material.

Plastic behavior of nuclear structural metals after cyclic prestraining

Abstract The plastic behavior of metals (SUS 304 stainless steel, 2 1 4 Cr-1Mo steel and Al-alloy) after cyclic prestraining is systematically and experimentally investigated in a state of plane stress that consists of axial and torsional stress (strain) components. A practical biaxial extensometer for use in cyclic and subsequently large strain tests is also developed. The stress level in reloading after cyclic prestraining is never below the corresponding initial stress-strain curve, regardless of the loading direction, even after cyclic softening. Initial plastic anisotropy does not disappear or become small due to cyclic prestraining, and may become strong, depending on the prestrain direction. The larger the cyclic strain hardening, smaller the work hardening coefficient in reloading. This suggests initial stress-strain relations should and can be used as basic data on materials when analyzing the strength and safety of a structure undergoing normal cyclic loading followed by abrupt overloading such as that occuring during an accident or earthquake.

Plastic behavior of metals after cyclic prestraining (3rd report, Deformation properties of reloading after cyclic prestraining)

The plastic behavior of metals (SUS 304, 2-1/4Cr-1 Mo steel Al alloy) after cyclic prestraining is systematically and experimentally investigated in a stress (strain) plane that consists of axial and torsional stress (strain) components. A useful multiaxial deformations sensor for both a cyclic test and a following large straining test is developed. The stress level in reloading after cyclic prestraining is never below the initial stress-strain curve, independently of the loading direction, even after cyclic softening, but may become strong depending on the prestraining direction, even after cyclic softening has occurred. An initial plastic anisotropy is never weak and never vanishes due to cyclic prestraining, but may become strong depending on the prestraining direction. The larger the cyclic strain hardening, the smaller the coefficient of work hardening in reloading. Therefore, it is suggested that the initial stress-strain relations should/can be used as basic material data for a strength and safty analysis of a structure that is subjected to both an usual cyclic load and an abrupt overload due to accident, earthquake and so on.

Plastic behaviour of metals and strain localization

Plastic behaviour of metals and strain localization

Scaling relationship in the log ?-log ? creep and stress-relaxation curves and the plastic equation of state

The log σ-log\( \in \) curves, obtained either during creep or stress-relaxation experiments, for different strain levels or initial stresses, frequently show a scaling behaviour. It will be discussed if the scaling relationship is a sufficient condition to ensure the existence of a state variable, dependent on σ and\( \in \). The results will be applied to some constitutive equations used to describe the plastic behaviour of metals and to creep and stressrelaxation data in Zircaloy-4. Finally, it is concluded that the constitutive equations considered define a state variable in a certain range of σ and\( \in \), limited by the values of the constants characteristic of the material.

On Mechanism of Induced Plastic Anisotropy of Polycrystalline Metals

The experimental results concerning the plastic behaviour of metals along the strain path with a corner have demonstrated some common and fundamental features of the induced plastic anisotropy of polycrystalline metals, for example, the fading memory, the saturation property of prestrain effect and the delay effect. It is shown that the mechanism of the induced plastic anisotropy is closely related with the internal stress due to the interaction among grains of deformed polycrystalline metals and the common features are related closely with the internal stress. Computations using a simple mathematical model of polycrystal proposed in relation to the idea of internal stress show a very good qualitative agreement with the experimental results obtained from some typical strain paths by using a thin-walled tubular specimen of brass.