FCC晶体中不均匀变形对空洞长大的影响

通过编制率相关有限元用户子程序,采用一个单胞模型研究了FCC晶体中孔洞在单晶及晶界的长大行为,分析了由于晶体取向及变形失配对孔洞长大和聚合的影响。研究结果表明：孔洞的形状和长大方向与晶体取向密切相关;晶界上孔洞的长大速度大于单晶中孔洞的长大速度;晶粒间的变形失配加速了晶界上孔洞的长大趋势,因而使材料易发生沿晶断裂,随着晶粒间取向因子差异的增加,孔洞越易沿着晶界长大。     

Analysis of transformation superplastic deformation in pure iron

Summary Transformation superplastic deformation in pure iron is analysed. The transformation phenomenology is first studied when the material is exposed to the constant-rate cyclic temperature histories between 20°C and 1100°C. Transformation diagrams (T-T-A, T-T-T, C-H-T and C-C-T diagrams) are shown to be constructed by means of the transformation kinetics employed. Change in the fraction of austenite, or of ferrite, during the cyclic process is calculated. The deformation in thin-walled tubular specimen is then estimated when it is exposed under a constant tensile or torsional stress to the temperature cyclings. Accumulation of the superplastic deformation due to A ₃ transformation is shown to be well simulated by the theory presented here.

---

Deformationsanalysis der Umwandlungsplastizität bei Eisen

Übersicht Die superplastische Deformation während der allotropen Umwandlung bei Eisen, A ₃ (Austenit Ferrit)-Umwandlung, wird analysiert. Die Umwandlungsphänomenologie wird theoretisch diskutiert, wenn das Material einer zyklischen Temperaturgeschichte zwischen 20°C und 1100°C ausgesetzt wird. Es wird gezeigt, daß man Umwandlungsdiagramme mit Hilfe der vorgeschlagenen Umwandlungskinetik gut konstruieren kann. Die Austenitbildung oder die Ferritbildung während des zyklischen Prozesses wird berechnet. Die Deformation von dünnwandigen, rohrförmigen Proben wird dann analysiert, wenn sie bei konstanter Zugspannung oder Torsionsspannung gleichzeitig durch ein zyklisches Temperaturfeld belastet werden. Die Ergebnisse zeigen, daß die akkumulierende Superplastizitätsdeformation von der Theorie gut beschrieben werden kann.

     

A molecular dynamics study of void growth and coalescence in single crystal nickel

Molecular dynamics simulations using Modified Embedded Atom Method (MEAM) potentials were performed to analyze material length scale influences on damage progression of single crystal nickel. Damage evolution by void growth and coalescence was simulated at very high strain rates (10⁸–10¹⁰/s) involving four specimen sizes ranging from ≈5000 to 170,000 atoms with the same initial void volume fraction. 3D rectangular specimens with uniform thickness were provided with one and two embedded cylindrical voids and were subjected to remote uniaxial tension at a constant strain rate. Void volume fraction evolution and the corresponding stress–strain responses were monitored as the voids grew under the increasing applied tractions.The results showed that the specimen length scale changes the dislocation pattern, the evolving void aspect ratio, and the stress–strain response. At small strain levels (0–20%), a damage evolution size scale effect can be observed from the damage-strain and stress–strain curves, which is consistent with dislocation nucleation argument of Horstemeyer et al. [Horstemeyer, M.F., Baskes, M.I., Plimpton, S.J., 2001a. Length scale and time scale effects on the plastic flow of FCC metals. Acta Mater. 49, pp. 4363–4374] playing a dominant role. However, when the void volume fraction evolution is plotted versus the applied true strain at large plastic strains (>20%), minimal size scale differences were observed, even with very different dislocation patterns occurring in the specimen. At this larger strain level, the size scale differences cease to be relevant, because the effects of dislocation nucleation were overcome by dislocation interaction.This study provides fodder for bridging material length scales from the nanoscale to the larger scales by examining plasticity and damage quantities from a continuum perspective that were generated from atomistic results.     

Thermomechanics of elastoplastic and superplastic deformation of metals

Using the process theory of A. A. Il’yushin, we consider the problem of determining the thermomechanical parameters of a material element for specified deformation and temperature-variation processes with allowance for the elastic, plastic, and viscous properties of superplastic deformation. The relations obtained are applicable for the case of arbitrary stresses and finite strains. The strain and stress measures are decomposed into elastic, plastic, and viscous components by classifying the processes into reversible, irreversible equilibrium, and nonequilibrium processes. Tula State University, Tula 300600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 164–172, September–October, 1999.     

Constitutive modeling of deformation and damage in superplastic materials

The superplastic deformation and cavitation damage characteristics of a modified aluminum alloy are investigated at a temperature range from 500 to 550°C. The baseline alloy is AA5083. Nominally this alloy contains about 4.5% Mg, 0.8% Mn, 0.2% Cr, 0.037% Si, 0.08% Fe and 0.025% Ti by weight. The experimental program consists of uniaxial tension tests and digital image analysis for measuring cavitation. The experiments reveal that evolution of damage is due to both nucleation and growth of voids. A viscoplastic model for describing deformation and damage in this alloy is developed based on a continuum mechanics framework. The model includes the effect of strain hardening, strain rate sensitivity, dynamic and static recovery, and nucleation and growth of voids. The model predictions compare well with the experimental results.     

Analysis of deformation mechanisms in superplastic yttria-stabilized tetragonal zirconia

There have been extensive experimental observations of changes in the apparent rate controlling creep parameters in studies on superplastic materials. The three most common explanations associated with these changes in the stress exponent, n, the activation energy Q and the inverse grain size exponent, p involve the effect of concurrent grain growth, the operation of a threshold stress or transitions in creep mechanisms. Each of these factors may influence experimental creep data in a similar manner. Therefore, a careful analysis of the consequences of all three factors must involve the development of a consistent set of experimental observations in order to adequately distinguish the effects of each. This paper discusses the role of concurrent grain growth, a threshold stress and transitions in creep mechanisms in superplastic materials. Specific attention is given to the analysis of data on superplastic yttria-stabilized zirconia ceramics for which an increase in n has been observed at low applied stresses. It is demonstrated that neither concurrent grain growth nor a threshold stress can account for all the relevant experimental observations in this material. It is concluded that the changes in rate controlling creep parameters are associated with the operation of two distinct sequential mechanisms as part of a grain boundary sliding process.     

Forming limit during superplastic deformation of sheet metals

ＦＯＲＭＩＮＧＬＩＭＩＴＤＵＲＩＮＧＳＵＰＥＲＰＬＡＳＴＩＣＤＥＦＯＲＭＡＴＩＯＮＯＦＳＨＥＥＴＭＥＴＡＬＳＤｕＺｈｉｘｉａｏ（杜志孝）;ＬｉＭｉａｏｑｕａｎ（李淼泉）;ＬｉｕＭａｂａｏ（刘马宝）;ＷｕＳｈｉｃｈｕｎ（吴诗惇）（Ｆａｃｕｌｔｙ４０２ｏ...     

Study of possible void nucleation and growth in solids in the framework of the Davis-Nadai deformation theory

In the framework of the Davis-Nadai deformation theory, we study the problem of a ball with a central cavity subjected to internal and external pressure. The solution is constructed in the reference configuration for the polynomial material deformation law with possible regard to matter conservation inside the cavity. The obtained solution is analyzed; it is mathematically proved that the limit load exists in the case of uniform compression, and a method for determining this load is given. It is also proved that a new void can be formed in a solid ball in the case of its extension, and the critical load of void formation is estimated. It is shown that the already existing spherical void cannot completely disappear under the action of external pressure (assuming that its shape is preserved and remaining in the framework of the continuity hypothesis).     

A note on the effect of surface energy and void size to void growth

Recent studies revealed that rapid void growth is the dominant failure mechanism in an elasto-plastic solid under high mean tensile stress. This paper studies the effect of the surface energy and void size to the void growth. The models of a thick spherical shell and a thick spherical column in void growth are analyzed and numerically estimated. The main conclusion from this study is that, for typical metals, the surface energy effect is negligible for voids larger than 100 nm in size, but it may become significant when the void size is on the order of 10 nm.     

Two mechanisms of ductile fracture: void by void growth versus multiple void interaction

Two distinct mechanisms of crack initiation and advance by void growth have been identified in the literature on the mechanics of ductile fracture. One is the interaction a single void with the crack tip characterizing initiation and the subsequent void by void advance of the tip. This mechanism is represented by the early model of Rice and Johnson and the subsequent more detailed numerical computations of McMeeking and coworkers on a single void interacting with a crack tip. The second mechanism involves the simultaneous interaction of multiple voids on the plane ahead of the crack tip both during initiation and in subsequent crack growth. This mechanism is revealed by models with an embedded fracture process zone, such as those developed by Tvergaard and Hutchinson. While both mechanisms are based on void nucleation, growth and coalescence, the inferences from them with regard to crack growth initiation and growth are quantitatively different. The present paper provides a formulation and numerical analysis of a two-dimensional plane strain model with multiple discrete voids located ahead of a pre-existing crack tip. At initial void volume fractions that are sufficiently low, initiation and growth is approximately represented by the void by void mechanism. At somewhat higher initial void volume fractions, a transition in behavior occurs whereby many voids ahead of the tip grow at comparable rates and their interaction determines initiation toughness and crack growth resistance. The study demonstrates that improvements to be expected in fracture toughness by reducing the population of second phase particles responsible for nucleating voids cannot be understood in terms of trends of one mechanism alone. The transition from one mechanism to the other must be taken into account.     

Dynamic void growth in rate-sensitive plastic solids

A dynamic void growth model in rate-sensitive plastic materials is derived. The constitutive relation of the matrix is in the overstress form proposed by Perzyna. When the rate of deformation sensitive parameter tends to zero, the Gurson model is retrieved. When the porous material element is under triaxial tension, the Carroll-Holt and Johnson models are retrieved. The normality condition of the plastic rate of deformation to the dynamic loading surface at constant equivalent rates of deformation (with the volumetric part also taken into account) is discussed, and it is shown that the normality rule no longer exists in general. Finally, an approximate expression of the dynamic loading surface that may be convenient for engineering applications is suggested.     

Dynamic void nucleation and growth in solids: A self-consistent statistical theory

We present a framework for a self-consistent theory of spall fracture in ductile materials, based on the dynamics of void nucleation and growth. The constitutive model for the material is divided into elastic and “plastic” parts, where the elastic part represents the volumetric response of a porous elastic material, and the “plastic” part is generated by a collection of representative volume elements (RVEs) of incompressible material. Each RVE is a thick-walled spherical shell, whose average porosity is the same as that of the surrounding porous continuum, thus simulating void interaction through the resulting lowered resistance to further void growth. All voids nucleate and grow according to the appropriate dynamics for a thick-walled sphere made of incompressible material. The macroscopic spherical stress in the material drives the response in all volume elements, which have a distribution of critical stresses for void nucleation, and the statistically weighted sum of the void volumes of all RVEs generates the global porosity. Thus, macroscopic pressure, porosity, and a distribution of growing microscopic voids are fully coupled dynamically. An example is given for a rate-independent, perfectly plastic material. The dynamics of void growth gives rise to a rate effect in the macroscopic material even though the parent material is rate independent.     

Effects of void band orientation and crystallographic anisotropy on void growth and coalescence

The effects of void band orientation and crystallographic anisotropy on void growth and linkage have been investigated. 2D model materials were fabricated by laser drilling a band of holes into the gage section of sheet tensile samples using various orientation angles with respect to the tensile axis normal. Both copper and magnesium sheets have been studied in order to examine the role of crystallographic anisotropy on the void growth and linkage processes. The samples were pulled in uniaxial tension inside the chamber of an SEM, enabling a quantitative assessment of the growth and linkage processes. The void band orientation angle has a significant impact on the growth and linkage of the holes in copper. As the void band orientation angle is increased from 0° to 45°, the processes of coalescence and linkage are delayed to higher strain values. Furthermore, the mechanism of linkage changes from internal necking to one dominated by shear localization. In contrast, the void band orientation does not have a significant impact on the void growth and linkage processes in magnesium. Void growth in these materials occurs non-uniformly due to interactions between the holes and the microstructure. The heterogeneous nature of deformation in magnesium makes it difficult to apply a coalescence criterion based on the void dimensions. Furthermore, the strain at failure does not show a relationship with the void band orientation angle. Failure associated with twin and grain boundaries interrupts the plastic growth of the holes and causes rapid fracture. Therefore, the impact of the local microstructure outweighs the effects of the void band orientation angle in this material.     

Coupling effects of void size and void shape on the growth of prolate ellipsoidal microvoid

The combined effects of void size and void shape on the void growth are studied by using the classical spectrum method. An infinite solid containing an isolated prolate spheroidal void is considered to depict the void shape effect and the Fleck-Hutchinson phenomenological strain gradient plasticity theory is employed to capture the size effects. It is found that the combined effects of void size and void shape are mainly controlled by the remote stress triaxiality. Based on this, a new size-dependent void growth model similar to the Rice-Tracey model is proposed and an important conclusion about the size-dependent void growth is drawn: the growth rate of the void with radius smaller than a critical radius r_c may be ignored. It is interesting that r_c is a material constant independent of the initial void shape and the remote stress triaxiality.The project supported by the National Natural Science Foundation of China (A10102006) and the New Century Excellent Talents in Universities of China. The English text was polished by Keren Wang.     

Micromechanical finite element calculations of temperature and void configuration effects on void growth and coalescence

We present micromechanical finite element results that quantify coalescence effects based upon temperature and different spatial arrangements of voids. We propose a critical intervoid ligament distance (ILD) to define void coalescence that is derived from micromechanical simulations in which void volume fraction evolves as a function of strain. Several parameters were varied using the temperature and strain rate internal variable plasticity model of Bammann–Chiesa–Johnson to determine the coalescence effects. The parameters include two types of materials with different work hardening rates (304L stainless steel and 6061T6 aluminum), three different temperatures (298, 400, and 600 K), several boundary conditions (force and displacement: uniaxial, plane strain, and biaxial), type of element used (plane strain and axisymmetric), different ILDs, and the number of voids (one and two void configurations). The present study provides a basis for macroscale modeling of coalescence which is briefly discussed.     

The effect of straining mode on void growth

Large strain finite element method is employed to investigate the effect of straining mode on void growth. Axisymmetric cell model embedded with spherical void is controlled by constant triaxiality loading, while plane-stress model containing a circular void is loaded by constant ratio of straining. Elastic-plastic material is used for the matrix in both cases. It is concluded that, besides the known effect of triaxiality, the straining mode which intensifies the plastic concentration around the void is also a void growth stimulator. Experimental results are cited to justify the computation results. This paper is jointly supported by the National Natural Science Foundation of China (19872064), the Chinese Academy of Sciences (KJ951-1-201) and the Laboratory for Nonlinear mechanics of Continuous Media of the Institute of Mechanics     

The size effect on void growth in ductile materials

We have extended the Rice-Tracey model (J. Mech. Phys. Solids 17 (1969) 201) of void growth to account for the void size effect based on the Taylor dislocation model, and have found that small voids tend to grow slower than large voids. For a perfectly plastic solid, the void size effect comes into play through the ratio εl/R₀, where l is the intrinsic material length on the order of microns, ε the remote effective strain, and R₀ the void size. For micron-sized voids and small remote effective strain such that εl/R₀?0.02, the void size influences the void growth rate only at high stress triaxialities. However, for sub-micron-sized voids and relatively large effective strain such that εl/R₀>0.2, the void size has a significant effect on the void growth rate at all levels of stress triaxiality. We have also obtained the asymptotic solutions of void growth rate at high stress triaxialities accounting for the void size effect. For εl/R₀>0.2, the void growth rate scales with the square of mean stress, rather than the exponential function in the Rice-Tracey model (1969). The void size effect in a power-law hardening solid has also been studied.     

A general yield criterion for engineering materials,depending on void growth

Summary Previously introduced yield criteria, taking into consideration the influence of internal dilation of the materials during yielding, were based on a conventional assumption of the influence of the hydrostatic component of stresses on the yielding process. They were fitted to the actual macroscopic behaviour of the materials and they were proved experimentally to predict the overall plastic behaviour of a great number of substances. In this paper a yield criterion was tested, which was based on the theory of void growth and coalescence in the vicinity of internal discontinuities of the material during yielding and fracture. The inverse dependence of yielding on the hydrostatic tension was incorporated, in the criterion and it was shown that an increase of the hydrostatic component creates a rapid decrease of fracture ductility.

---

Sommario I criteri di snervamento precedentemente introdotti, che considerano l'influenza della dilatazione interna dei materiali sullo snervamento, erano basati sull'assunzione convenzionale che la componente idrostatica del tensore degli sforzi avesse influenza sul processo di plasticizzazione. In accordo con l'attuale comportamento macroscopico del materiale, è stato provato sperimentalmente che essi predicono il comportamento plastico totale di un gran numero di sostanze. In questo articolo viene proposto un criterio basato sulla teoria di crescita dei vuoti e di coalescenza in vicinanza di discontinuità interne del materiale durante lo scorrimento plastico e la frattura. Nel criterio è contenuta la dipendenza inversa della plasticizzazione dalla tensione idrostatica, e viene dimostrato che l'aumento della componente idrostatica crea una rapida diminuzione della duttilità della frattura.

     

RVE-based studies on the coupled effects of void size and void shape on yield behavior and void growth at micron scales

The present paper extends the Gurson and GLD models [Gurson, A.L., 1977. Continuum theory of ductile rupture by void nucleation and growth, Part I—yield criteria and flow rules for porous ductile media. J. Mech. Phys. Solids 99, 2–15; Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing non-spherical voids—case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754; Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing non-spherical voids—case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Technol. 116, 290–297] to involve the coupled effects of void size and void shape on the macroscopic yield behavior of non-linear porous materials and on the void growth. A spheroidal representative volume element (RVE) under a remote axisymmetric homogenous strain boundary condition is carefully analyzed. A wide range of void aspect ratios covering the oblate spheroidal, spherical and prolate spheroidal void are taken into account to reflect the shape effect. The size effect is captured by the Fleck–Hutchinson phenomenological strain gradient plasticity theory [Fleck, N.A., Hutchinson, J.W., 1997. Strain gradient plasticity. In: Hutchinson, J.W., Wu, T.Y. (Eds.), Advance in Applied Mechanics, vol. 33, Academic Press, New York, pp. 295–361]. A new size-dependent damage model like the Gurson and GLD models is developed based on the traditional minimum plasticity potential principle. Consequently, the coupled effects of void size and void shape on yield behavior of porous materials and void growth are discussed in detail. The results indicate that the void shape effect on the yield behavior of porous materials and on the void growth can be modified dramatically by the void size effect and vice versa. The applied stress triaxiality plays an important role in these coupled effects. Moreover, there exists a cut-off void radius r_c, which depends only on the intrinsic length l₁ associated with the stretch strain gradient. Voids of effective radius smaller than the critical radius r_c are less susceptible to grow. These findings are helpful to our further understanding to some impenetrable micrographs of the ductile fracture surfaces.