Plastic Deformation History Research Articles

유한요소법과 연성파괴이론에 의한 AZ31합금 판재의 온간 드로잉 공정에서의 파단예측

Abstract The forming failure of AZ31 alloy sheet during deep drawing processes was predicted by the FEM and ductile fracture criteria. Uniaxial tensile tests of round-notched specimens and FE simulations were performed to calculate the critical damage values for three ductile fracture criteria. The critical damage values for each criterion were expressed as a function of strain rate at various temperatures. In order to determine the best criterion for failure prediction, Erichsen cupping test under isothermal conditions at 250℃ were conducted. Based on the plastic deformation histories obtained from the FE analysis of the Erichsen cupping tests and the critical damage value curves, the initiation time and location of fracture were predicted under bi-axial tension deformation. The results indicate that the Cockcroft-Latham criterion had good agreement with the experimental data. In addition, the FE analysis combined with the criterion was applied to another deep drawing process using an irregular shaped blank and these additional results were verified with experimental tests.

Failure Prediction in Drawing Processes of Mg Alloy Sheet by the FEM and Ductile Fracture Criterion

In this work, in order to predict the forming failure of AZ31 magnesium alloy sheet in drawing process at elevated temperatures, a series of square cup tests at various temperatures and FE analyses were carried out. The critical damage values and the mechanical properties dependent on strain rates and temperatures were evaluated from uniaxial tensile tests and those were utilized to the forming failure prediction using FE analysis. Based on the plastic deformation history obtained from FE analysis and Cockcroft and Latham’s ductile fracture criterion, the fracture initiation time and location were predicted and verified with the experimental results.

High-efficiency automated line for precise cold rolling of bearing rings

751 New metalworking methods are essential to rapid progress in Russian manufacturing. An important development in manufacturing is the replacement of cutting processes by pressure treatment of cold metals, such as cold rolling and the profiling of solids of revo� lution (knurling). The history of plastic deformation by rolling extends back over 120 years, and Russian specialists have made significant contributions to its more recent development. Compared to cutting, knurling has the following benefits: considerably reduced metal consumption; improved productivity, precision, and final surface roughness; reduced operating costs (for the cutting tool and other equipment); reduced demand for production space; and reduced costs and amortization. The preci� sion of profile elements produced by rolling matches

Modeling of Dynamically Loaded Open-Cell Metallic Foams: Yielding, Collapse, and Strain Rate Effects

Open-cell metallic foams exhibit properties desirable in engineering applications requiring mitigation of the adverse effects resulting from impact loading; however, the history dependent dynamic response of these cellular materials has not been clearly elucidated. This article contributes an approach for modeling the response of dynamically loaded open-cell metallic foams from ligament level to unit cell level to specimen level. The effective response captures the localized chaotic collapse phenomena through ligament reorientation at cell level while maintaining the history of plastic deformation at ligament level. First, the phenomenological elastoplastic constitutive behavior of the ligaments composing the unit cell is modeled. Then, using the constitutive ligament model, the effective unit cell response is obtained from a micromechanical model that enforces the principle of minimum action on a representative 3D unit cell. Finally, the macroscopic specimen response is predicted utilizing a finite element analysis program, which obtains the response at every Gauss point in the mesh from the microscopic unit cell model. The current communication focuses on the ability of the model to capture the yielding and collapse behaviors, as well as the strain rate effects, observed during impact loading of metallic foams.

Themo-mechanical and microstructural modeling of friction stir welding of 6111-T4 aluminum alloys

Plastic deformation and thermal history as well as microstructure evolution of friction stir welded 6111-T4 aluminum alloys were numerically simulated. Material and heat flow during friction stir welding were calculated considering the momentum balance equation and energy balance equation under the steady state condition. Based on the calculated temperature history, the coupled nucleation, growth, and coarsening of precipitates were simulated using microstructural modeling, as proposed by Myhr et al. [7,8]. Finally, the distribution of precipitates was used to calculate the mechanical properties of the weld zone, particularly the yield stress, based on the dislocation theory. The results compared well with the measurements, suggesting that the method can be applicable to predict yield stress.

Numerical Simulation of Friction Stir Welding of AA6111-T4 Sheets

In an effort to develop the numerical modeling method to optimize the friction stir welding process for quality products, the plastic deformation and thermal histories of friction stir welded AA6111-T4 sheets were numerically simulated. Material and heat flow during friction stir welding were calculated considering the momentum and energy balance equations under the steady state condition. The results agreed well with the temperature measurements, suggesting that the method can be applicable to optimize the friction stir welding process, if proper mechanical and thermal properties of materials are available.

Cyclic Mechanical and Fatigue Properties of OCTG Materials

This article, written by Assistant Technology Editor Karen Bybee, contains highlights of paper SPE 97775, "Cyclic Mechanical and Fatigue Properties for OCTG Materials," by T.M.V. Kaiser, SPE, and V.Y.B. Yung, SPE, Noetic Engineering Inc., and R.M. Bacon, Imperial Oil Resources, prepared for the 2005 SPE International Thermal Operations and Heavy Oil Symposium, Calgary, 1-3 November. Much of the design for well structures subjected to high-amplitude cyclic loading is based on material assumptions that extrapolate strength properties from uniaxial, monotonic tests to conditions where cyclic, multiaxial stresses are imposed. The full-length paper presents results from cyclic testing on common oil-country tubular goods (OCTG) materials and shows the difference between physical behavior measured under cyclic-loading conditions and theoretical behavior extrapolated by numerical modeling. Modeling theories for plastic deformation are discussed, including their limitations and relevance in a cyclic-loading environment. Introduction Most thermal-recovery oil wells in western Canada operate by use of cyclic steam stimulation (CSS) or steam-assisted gravity drainage. Both methods impose thermal cycles on well structures, particularly the intermediate casing. Thermal expansion is constrained by the formation and cement, producing loads that exceed tubular yield strength when the well is heated. Localization mechanisms amplify strain magnitude, imposing additional plastic-fatigue loads at discrete locations in the well. Thermal-well casing designs have evolved through more than 30 years of operating experience, and much of the computer modeling that describes casing performance is based on uniaxial material properties, extrapolated to multidimensional and cyclic behavior through engineering models. Cyclic material-properties data are very sparse, particularly in the temperature range common in thermal-recovery wells. Furthermore, plastic-fatigue-life information for materials commonly used in well construction is difficult to obtain. Such information, however, is required to make reliable predictions of certain deformation mechanisms and associated fatigue life for wells exposed to cyclic, thermally imposed deformations. A test program for characterizing cyclic material properties was undertaken to evaluate both cyclic mechanical properties and low-cycle fatigue life. Test results demonstrate consistency indicative of reliable material characterization that can be applied in analysis models and component life assessments. The observed cyclic behavior also demonstrates material characteristics significantly different from those predicted through engineering models using uniaxial, monotonic material properties for input. This has important implications for selection of steels used in thermal-well designs and for implementing techniques to mitigate casing-deformation effects. Background Post-Yield Plasticity. Much of the work to characterize metal post-yield behavior was developed to support structural analysis under conditions where the load exceeds that required to yield some components. Material properties usually are determined from uniaxial coupon tests that give elastic modulus, yield strength, and post-yield strengthening or hardening. Structural modeling, whether analytic or numeric, requires that behavior measured in one dimension be extended into a multidimensional stress state. Furthermore, plastic behavior is load-path dependent (i.e., the stress state is not defined uniquely by the strain, but rather depends on the history of plastic deformation).

Effect of cold rolling on the indentation deformation of AA6061 aluminum alloy

The indentation behavior of cold-rolled AA6061 Al alloy was investigated. Following the approach suggested by Tabor, indentation stress–indentation strain curves were constructed and analyzed. The indentation stress required to create the same indentation strain increases with an increase in the reduction of thickness, suggesting a strong effect of plastic deformation history on the deformation behavior of materials. Through the dislocation dynamics, the evolution of the dislocations underneath the indentation was correlated with the plastic deformation history and the indentation load. The plastic energy dissipated in indentation was then calculated and found to be proportional to the 3/2 power of the indentation load and the 3/4 power of the average dislocation density underneath the indentation. The ratio of the dissipated plastic energy to the total energy in the indentation was demonstrated to be a function of the deformation state in materials, independent of the indentation load.

Two-scale analysis for deformation-induced anisotropy of polycrystalline metals

The anisotropic macroscopic mechanical behavior of polycrystalline metals is characterized by incorporating the microscopic constitutive model of single crystal plasticity into the two-scale modeling based on the mathematical homogenization theory, which enables us to derive both micro- and macro-scale governing equations. The two-scale simulations are conducted to evaluate the macroscopic anisotropy induced by microscopic plastic deformation histories of the polycrystalline aggregate. In the simulations, the representative volume element (RVE) composed of several crystal grains is uniformly loaded in one direction, unloaded to macroscopically zero stress in a certain stage of deformation and then re-loaded in the different directions. The last re-loading calculations provide different macroscopic responses of the RVE, which can be the appearance of material anisotropy. We then try to examine the effects of the intergranular and intragranular behaviors on the anisotropy by means of various illustrations of microscopic plastic deformation process without referring to the change of crystallographic orientations.

High strain-rate tensile testing and viscoplastic parameter identification using microscopic high-speed photography

A combined experimental/numerical method for determination of constitutive parameters in high strain-rate material models is presented. Impact loading, using moderate projectile velocities in combination with small specimens (sub mm) facilitate tensional strain rates in the order of 10 4–10 5 s −1. Loading force is measured from one-dimensional wave propagation in a rod using strain gauges and deformation is monitored with a high-speed camera equipped with a microscope lens. A sequence of digital photographs is taken during the impact loading and the plastic deformation history of the specimen is quantified from the photographic record. Estimation of material parameters is performed through so called inverse modelling in which results from repeated FE-simulations are compared with experimental results and a best choice of constitutive parameters is extracted through an iterative optimisation procedure using the simplex method. Results are presented from a preliminary tension test of a mild steel (A533B) at a strain rate well over 10 4 s −1. The sensitivity of the evaluated material parameters to errors in measured quantities is studied. The method, especially the optical technique for measurement of deformation will be further developed.

Sillimanite-bearing shear zones in syntectonic leucogranite: fluid-assisted brittle–ductile deformation under amphibolite facies conditions

In the Imja Kola valley (eastern Nepal), Miocene peraluminous leucogranite dykes were emplaced within transtensional shear zones synchronously with regional amphibolite–facies metamorphism in the metamorphic host rocks. Within the dykes the magmatic foliations, parallel to the metamorphic schistosity, are cross-cut by thin (millimetre to centimetre size) shear zones, which are made up of prismatic and/or fibrolitic sillimanite with a minor amount of white mica. These structures have a heterogeneous distribution and form networks of strongly deformed and foliated layers wrapping around poorly deformed granitic pods. The textural and strain features are consistent with development of sillimanite shear zones as a result of heterogeneous deformation and fluid action, which allowed the replacement of strained magmatic minerals such as feldspar and biotite by means of incongruent pressure solution. The described example illustrates that nucleation and development of heterogeneous shear zones under amphibolite facies conditions, is also strongly favoured by brittle fracturing and fluid action at the grain-scale along pre-existing planes of weakness. The growth of cracks and fractures can be regarded as a sequence of short lived brittle events, due to work hardening, which punctuate a history of plastic deformation.

Equations of growth of fatigue cracks in inhomogeneous plates

We propose a computational model for the determination of the kinetics of propagation of fatigue cracks in plates whose material has inhomogeneous mechanical characteristics and fatigue fracture resistance. We also take into account the history of plastic deformation of the plate. The model is based on the energy criterion of fatigue fracture of materials. We deduce a system of differential equations describing the kinetics of fatigue cracks in inhomogeneous plates and present the solutions of two particular problems obtained by using the proposed model.

Endochronic Theory of Continuum Damage Mechanics

The constitutive framework presented accounts for the coupling between the damage process and the plastic deformation process. The model build its basis on the thermodynamic equivalence of an actual damaged continuum and an equivalent fictitious undamaged continuum. It uses damage internal state variables that are independent of the damage measure and it uses corotational derivatives of damage descriptors. An endochronic theory is used to derive explicit equations. Two intrinsic times are used. The first intrinsic time is used to describe the plastic deformation history of a material. The second intrinsic time is used to depict the damage history. The constitutive equations of this theory are continuous without discontinuities, and the yield conditions are not needed in the numerical calculation. The proposed model is verified against reported results for one-dimensional, monotonic and cyclic loading of concrete and mortar specimens subjected to uniaxial tension and compression.

Simulation of Berkovich nanoindentation experiments on thin films using finite element method

The Finite element technique is applied for studying the very complex stress-strain field of thin hard coatings subjected to a nanoindentation process. Berkovich indentation experiments were simulated with the ABAQUS finite element software package. The investigated system was titanium nitride on high speed steel as an example of a hard film on a softer substrate. The numerical analysis allowed the plastic deformation history during indentation to be followed. In particular, it was possible to correlate the onset of plastic deformation in the substrate with the shape of the loading curve. The system was simulated by an axisymmetric model in which the conical indenter has the same contact area as the Berkovich indenter. A six-fold symmetric three-dimensional model was also defined for testing the suitability of the previous model. The indenter was modeled either as a rigid surface or as a deformable diamond tip. Comparison between the experimental data and numerical results demonstrated that the finite element approach is capable of reproducing the loading-unloading behavior of a nanoindentation test. The film hardness of TiN/HSS specimens was numerically calculated for different indentation depths. It was shown that the presence of the substrate affected the hardness measurement for relative indentation depths greater than about 15% of the film thickness.

INELASTIC MEMORY VERSUS VISCOPLASTICITY OF CONTINUOUSLY DAMAGED MATERIALS

In the paper the principle of determinism based on inelastic (i.e. damage– plastic) deformation history is formulated. In the case of fading memory materials of integral (leading to a general endochronic theory) and differential type (leading to standard viscoplasticity with a non-associate flow rule) are obtained from a general functional representation. Rotations of natural state local reference configuration are discussed and issues concerning plastic spin and Drucker’s normality are discussed. INTRODUCTION The objective of this paper is to consider a relation between inelastic materials with internal variables and damaged inelastic materials with memory. If an evolution equation for plastic strain rate is given for the first class of materials, then its integration leads to the description represented by integrals whose kernels are responsible for a plastic memory. Here the opposite and more difficult way is aimed: to see how functionals appearing in a description of damaged inelastic materials with memory may be transformed into the corresponding evolution equations. For a correct constitutive theory a geometric description able to desribe properly most important microstructural changes during an inelastic deformation process is indispensable. This is done in the following section, whereas the last section is reserved for formulation of the theory. KINEMATICAL ISSUES Consider a crystalline body, B, in a real configuration (ψt) with defects (such as dislocations, voids, impurities) and an inhomogeneous temperature Published in Journal of the Mechanical Behavior of Materials, Vol.4, No.4, p.331–341, 1993.

Constitutive modelling of nonproportional cyclic plasticity

A multiplicative hardening function and a unified evolution rule of the hardening factors are proposed. The hardening factorf1 is introduced to describe cyclic hardening with respect to the plastic strain range, whilef2 andf3 describe, respectively, instantaneous and hereditary additional hardening with respect to the nonproportionality of the plastic strain path. Two material dependent memory parametersa1 anda3 are introduced to keep the memory of the largest cyclic and additional hardening in the previous plastic deformation history. Different hardening mechanisms are then embedded into a thermomechanically consistent constitutive equation through the hardening function. The constitutive response of 304 and 316 stainless steels subjected to biaxial nonproportional cyclic loading is analyzed and the proposed model is critically verified by comparing the results with experimental results obtained by Tanaka et al., and Ohashi et al.

The ductile fracture of metals: A microstructural viewpoint

A review of the literature on the ductile fracture of metals and alloys reveals almost immediately that the majority of investigations approach the topic from a fracture mechanics point of view and that papers based entirely on microstructural research are rare. In a substantial number of papers the two viewpoints are combined. Correspondingly, Section 2 covers some aspects of continuum theory which would be of value in regard to this review and also includes a few points on the other extreme, namely the atomic approach to fracture. The microstructural regime covers the broad area between these two concepts. Since ductile fracture depends on the history of plastic deformation in the specimen, an outline of a successful theory of work hardening has been included. Also, it should not be overlooked that the experimental tools for microstructural investigations developed rapidly during the past decade and are briefly reviewed in Section 2.4. Section 3 addresses rupture since this mechanism includes the fundamental processes which govern ductile fracture generally and in particular the final separation. The most common mode, fibrous fracture, is reviewed in Section 4. Continuum mechanics still plays the major role in fibrous fracture research, although microstructural considerations are becoming a greater part of this work. In the final section a variety of topics which have a bearing on a more comprehensive understanding of ductile fracture (such as delamination and cleavage fractures, the role of voids in microcrack initiation, the energy of dislocation cell walls, and the thickness of microtensile specimens and the rate of straining for in situ experiments) are emphasized and discussed critically. A brief perspective summary pointing out the significant role of rupture processes which also govern the final separation of fibrous fracture concludes Section 5.

Effects of Plastic Deformation and Thermal History on σ Phase Precipitation in Duplex Phase Stainless Steels

Effects of hot or cold deformation and thermal history on theσ phase0 precipitation in (A) a 25Cr-7Ni-3Mo and (B) a 23Cr-6Ni steels with ferrite/austenite (α/γ) duplex structure have been studied. Results obtained are as follows:(1) The incubation time for the σ phase precipitation in Steel B was a couple of orders of magnitude longer than that in Steel A. This should be attributed to the difference in chemical composition between two steels, especially in a phase, where the majority of σ phase is known to precipitate.(2) σ phase precipitation is enhanced by hot work or thermal strain as well as cold work. The enhancing effect of cold work is predominant, and the precipitation of σ particles is observed in γ grains as well as in α grains.(3) The precipitation of σ phase is retarded by the prior heating history before aging; (a) heating at the α single phase region or (b) remelting. Especially the effect of the treatment (b) is remarkable. These retardation effects can be ascribed to homogenization of alloying elements by these heat treatments. The difference between the cases of (a) and (b) is thought to result from the degrees of their homogeneities.

Dynamic response of a slab of elastic-viscoplastic material that exhibits induced plastic anisotropy

Various 2-dimensional problems of the dynamic loading of a slab are solved for a material characterization that is elastic-viscoplastic and exhibits anisotropic work-hardening. The governing constitutive equations are based on a unified formulation which requires neither a yield criterion nor loading or unloading conditions. They include multi-dimensional anisotropic effects induced by the plastic deformation history. The theory also considers plastic compressibility which depends on the extent of the anisotropy. A numerical procedure for solving the equations is developed which incorporates the history dependent anisotropic hardening effects. Cases considered are the dynamic penetration of a slab by a rigid cylindrical indenter, and a distributed force rapidly applied over part of the slab surface. Both conditions of fixed and free rear surfaces of the slab are examined. A uniaxial problem is also considered in which different bases for the anisotropic hardening law are examined.

Penetration calculations and measurements for a layered soil target

AbstractA tow‐dimensional finite difference wave propagation code was used to analyse the impact of a rigid, ogival‐nosed penetrator with a target consisting of thin alternating layers of silt, sand, and clay. The response of the idealized target was described with an elastic‐plastic constitutive model depending upon two stress invariants and the history of plastic deformation. Interfacial friction between the penetrator and target was assumed to be negligible.Comparisons are made of calculated results and those of nominally similar experiments conducted at the Watching Hill test site in Alberta, Canada. Analysis of these comparisons reveals that numerical methods like the one employed in this study can yield insight into penomena, as well as suggesting possible improvements in the calculation technique.