Instantaneous Plastic Deformation Research Articles

Mechanism of accelerated dissolution of mineral crystals by cavitation erosion

Cavitation, a phenomenon produced by a moving fluid, is ubiquitous in the water environment of the Earth’s surface and its related mechanical action in the process of cavitation leads to the widespread erosion of rock in nature. Although the mechanical action of flowing water body that accelerates the rock mass loss and fragmentation of rock (abrasion, erosion, and etching) and other phenomena have been much studied, its acceleration of mineral crystal dissolution is rarely reported. The physical mechanism of effect is not yet clear. The cavitation bubble produced in the cavitation process is at the micron level, and its related mechanical action leading to the accumulation of rock mineral dissolution is manifested in time and space in the process of the chemical element’s migration between water and rock minerals. Cavitation erosion may be one of the important driving forces for the migration of geochemical elements within the lithosphere and hydrosphere. In this paper, based on the crystal dissolution stepwave dynamic theory and the theoretical derivation and calculation of Gibbs free energy change of the mineral crystals plastic deformation which caused by the mechanical action of cavitation erosion, we give the possible mechanism of accelerating the transient dissolution of mineral crystals by cavitation erosion—the cavitation bubbles on the surface of the near crystal release the high speed micro-jet and shock wave perpendicular to the surface during the collapsing, in which the water hammer pressure produced by micro-jet at the solid–liquid interface causes instantaneous plastic deformation on the crystal surface under the condition that it is larger than the yield stress of the crystal. Under the influence of the thermal effect of the plastic deformation process and the change of Gibbs free energy (the dislocation elastic strain energy of plastic deformation on the crystal surface may be included), the local instantaneous dissolution rate of the mineral surface is accelerated. The continuous cavitation erosion eventually causes fracture and breaking of the mineral crystal, meanwhile, the Gibbs–Thomson effect may enhance the dissolution of mineral crystals more prominently. At the same time, the correctness of the mechanism is verified qualitatively by the acoustic cavitation experiment with the same erosion mechanism.

Effects of inclusions and pores on plastic and viscoplastic deformation of rock-like materials

The aim of this paper is to study effects of inclusion and pores on plastic and viscoplastic deformation of rock-like materials. We shall consider a class of clayey rocks with two separate scales of microstructure. At the mesoscopic scale, the material is constituted by a continuous matrix and embedded mineral inclusion. At the microscopic scale, the continuous matrix is a porous medium composed of a solid phase and spherical pores. Macroscopic deformation behavior of the material is determined by using a two-step homogenization procedure. An analytical plastic yield criterion is used for the porous matrix in the first step. It is assumed that the porous matrix exhibits both instantaneous plastic deformation and delayed viscoplastic deformation, which are described by a unified formulation. The plastic criterion is extended to serve as the viscoplastic loading function. At the mesoscopic scale, we shall investigate influences of inclusion stiffness, shape, orientation and volume fraction on plastic and viscoplastic deformation. Due to the absence of analytical solutions, we shall propose an extended Fast Fourier Transform method (FFT) to solve the nonlinear homogenization problem of the unit cell exhibiting time-dependent plastic deformation. A series of numerical simulations are performed and the obtained results show that the proposed numerical model is able to bring a finer description of complex microstructure effect than most analytical models. Finally, the efficacy of this numerical model is checked through comparisons between numerical results and experimental data in triaxial compression creep and relaxation tests on claystone.

Influence of loading rate on the mechanical performance of metallic glass

Amorphous metallic glass Cu47Ti35Zr11Ni6Si1 was investigated by load-control nanoindentation experiments using the cube corner indenter tip over a wide range of loading rates. The indentation hardness was calculated using different methods either from the loading curves or indent area. Pop-in events were observed on the loading part of the indentation curves mainly at lower rates of loading. Instantaneous plastic deformation decreases with increasing loading rate according to a power law. At high loading rate the instantaneous deformation is suppressed by continuous plastic deformation and no well-developed pop-ins are observed. The morphology of shear bands in the pile-up area of indents showed no correlation with the pop-in event population of the nanoindentation curves and the loading rate.

Shear Band Morphology of Indented Region in Cu-Based Metallic Glass

Plastic deformation after indentation of the metallic glass Cu47Ti35Zr11Ni6Si1 at different loading conditions was examined. Discontinuities on the loading curves were observed, the magnitude of which depends on the loading rate. The presence of these discontinuities is influenced by the precise shape of the indentation tip. At lower loading rates and using a cube corner indenter tip the discontinuities on the loading curves are more pronounced. An increase of the loading rate tends to diminish instantaneous plastic deformation as appear by pop-ins. Using a Berkovich type indenter tip the plastic deformation is more steady. It is concluded that the final morphology of the pile-up area strongly depends on the geometry of the indenter tip, whereas no correlation between discontinuities in the loading part of the indentation curve and the formation of shear band patterns was observed.

Deformation Behavior Immediately After Indentation Load Change in Ultrafine-Grained Al-Mg Solid Solution Alloys

Instrumented indentation tests were performed to study how grain boundaries and solute atoms affect creep and instantaneous plastic deformation in ultrafine-grained (UFG) Al-Mg solid solution alloys with average grain size d = 0.3 − 1.0 μm at T = 373 K. In the results for Al-1.0 mol% Mg, the degree of instantaneous plastic displacement generated with a rapid increase in the load was smaller when the grain diameter was smaller. On the other hand, creep occurs more readily in materials with a smaller grain diameter. When the load was rapidly decreased during creep, the indenter displacement gradually decreased over time. The degree of reverse creep that occurs is greater when the grain diameter is smaller. In light of these test results and reports in the related literature, reverse creep is thought to occur because of inverted movement of piled-up dislocations near the grain boundaries. For the case of Al-xMg (x = 0.5, 1.0, 2.0 mol%), the results show that as the solute concentration increases, the occurrence of instantaneous plastic deformation, creep, and reverse creep becomes less likely. Overall, the results indicate that the plastic deformation behavior obtained by the testing conditions of present study for UFG Al-Mg alloys could be explained based on understanding of the behavior of course-grained materials.

Study on the mechanism of diametral cladding strain and mixed-oxide fuel element breaching in slow-ramp extended overpower transients

Cladding strain caused by fuel/cladding mechanical interaction (FCMI) was evaluated for mixed-oxide fuel elements subjected to 70–90% slow-ramp extended overpower transient tests in the experimental breeder reactor II. Calculated transient-induced cladding strains were correlated with cumulative damage fractions (CDFs) using cladding strength correlations. In a breached high-smeared density solid fuel element with low strength cladding, cladding thermal creep strain was significantly increased to approximately half the transient-induced cladding strain that was considered to be caused by the tertiary creep when the CDF was close to the breach criterion (=1.0), with the remaining strain due to instantaneous plastic deformation. In low-smeared density annular fuel elements, FCMI load was significantly mitigated and resulted in little cladding strain. The CDFs of the annular fuel elements were lower than 0.01 at the end of the overpower transient, indicating a substantial margin to breach. A substantial margin to breach was also maintained in a high-smeared density fuel element with high strength cladding.

Compressive Creep Behaviour of Cast Magnesium Under Stresses Above the Yield Strength and The Resultant Texture Evolution

Creep behaviour of commercial purity cast magnesium with preferred orientation was examined in compression at 100, 125 and 150°C and 35 and 50 MPa. The as-cast structure is composed of large columnar grains in which prismatic poles are parallel to the longitudinal direction. Cylindrical compression specimens were prepared from the cast material in the way that columnar grains were almost perpendicular to the compressive loading direction. Steady-state creep rate increased from -2 xl x 1 0-7/s to 5 x 10-7/s at 35 MPa and from 5.7 x 1O--7/s to 2 x 10- 6/s at 50 MPa with increasing temperature from 100 to 150 °C. The apparent activation energy, Qc, was determined to be 34 kJ/mol at 50 MPa and 29kJ/mol at 35 MPa. The stresses used were above the yield strength of the cast Mg and instantaneous plastic deformation occurred at creep loading. It was noticed that creep under the aforementioned conditions changed the initial grain orientation. Such evolution of orientation was stronger at higher temperatures. Some evidence of grain boundary serrations was also observed after creep and these were attributed to creep-deformation due to strain-induced grain boundary migration.

Viscoelasto-plastic rheological experiment under circular increment step load and unload and nonlinear creep model of soft rocks

The viscoelastic-plastic creep experiments on soft ore-rock in Jinchuan Mine III were performed under circular increment step load and unload. The experimental data were analyzed according to instantaneous elastic strain, visco-elastic strain, instantaneous plastic strain and visco-plastic strain. The result shows that instantaneous deformation modulus tends to increase with the increase of creep stress; soft rocks enhance the ability to resist instantaneous elastic deformation and instantaneous plastic deformation during the multi-level of load and unload in the cyclic process. In respect of specimen JC1099, the ratio of visco-elastic strain to visco-plastic strain varies from 3.15 to 6.58, and the ratio has decreasing tendency with stress increase as a whole; creep deformation tends to be a steady state at low stress level; soft rocks creep usually embodies accelerated creep properties at high stress level. With the damaging variable and the hardening function introduced, a nonlinear creep model of soft rocks is established, in which the decay creep is described by the nonlinear hardening function H of viscidity coefficient. The model can describe the accelerated creep of soft rocks since the nonlinear damaging evolvement variable D of deformation parameter of rocks is introduced. Three stages of soft rocks creep can be described with the uniform creep equation in the nonlinear creep model. With this nonlinear creep model applied to the creep experiments of the ore-rock of Jinchuan Mine III, the nonlinear creep model’s curves are in good agreement with experimental data.

Elastoplastic deformation of a porous rock and water interaction

In this paper, a new constitutive model is proposed for the description of elastoplastic behaviour of a porous chalk, including creep deformation and effect of water saturation. The chalk is represented by a two-phase porous composite, a homogenized equivalent matrix including solid grains, different contacts between grains, and a connected porosity. Two plastic flow mechanisms are identified: inelastic pore collapse at high confining pressure and plastic shearing at low confining pressure. The plastic yield stress of the equivalent solid matrix and the porosity are used as the fundamental parameters in the macroscopic yield function for pore collapse mechanism. The plastic shearing mechanism describes plastic distortion and failure by the formation of shear bands. Influences of water saturation on the mechanical behaviour are decomposed into a short term and a long term effect. Water saturation induces the diminution of capillary pressure in liquid contact, leading to an instantaneous plastic deformation. As a long term effect, water saturation enhances the pressure dissolution of cemented contacts, resulting in progressive weakening of pore collapse yield stress and failure strength. Comparisons between numerical predictions and experimental data are presented in different loading conditions to verify the predictive capacity of the proposed model.

Experimental and computational study on the load-jump tests of Al–Mg solid–solution alloy using instrumented indentation technique

Constant-load tests and load-jump tests were carried out using a microindenter in Al–5.3 mol% Mg solid–solution alloy. When the representative stress σ ¯ beneath the indenter decreases to a critical stress level, σ ¯ c ≅ 61 MPa , during indentation creep at 573 K, the stress exponent n for creep changes from 5 ( σ ¯ > σ ¯ c ) to 3 ( σ ¯ < σ ¯ c ). With load-jump tests in the stress range of n = 3, instantaneous plastic deformation (IPD) is initiated at stresses of σ ¯ > 54 MPa or more. When IPD does not occur, the n value obtained from load-jump tests agrees fairly well with that of constant-load tests. The experimental results are supported by finite-element simulations on load-jump tests. In order to evaluate the n value robustly by the load-jump test, the test should be conducted under a loading condition at which only elastic deformation takes place or no IPD occurs.

計装化押込み試験法によるＡｌ‐Ｍｇ固溶体のクリープ律速過程の遷移検出

Indentation creep tests of an Al-5.3 mol% Mg solid-solution alloy were performed using a microindenter in order to examine whether creep properties can be extracted accurately from a testpiece which is as small as a rice grain. A conical indenter was pressed into a surface with a load of 0.39 N at temperatures ranging from 546 to 590 K. When the average equivalent stress σm in the region beneath the indenter decreases to a critical stress σc during the creep indentation, the creep stress exponent n changes from 4.9 to 3.0. The measured σc-value decreases from 122 to 52 MPa with increasing temperature, while the corresponding indentation strain rate εc increases from 1.22×10-3 to 2.00×10-3 s-1. The temperature dependence of σc and εc is almost in agreement with the results derived from dislocation theory. The activation energy Q for creep in the stress range H (σm>σc) is approximately equivalent to that for the lattice diffusion of pure aluminum, 144 kJ mol-1. The Q-value in the stress range M (σm<σc) is close to the activation energy for the mutual diffusion of this alloy, 130 kJ mol-1. With load-jump tests at T=573 K, indentation load was abruptly changed from 0.39 N to various values ranging 0.19-0.59 N. In the stress range H, instantaneous plastic deformation (IPD) takes place evidently even when the load increment ΔF is very small. In the stress range M, the IPD does not occur when ΔF is within a certain value. However, the occurrence of IPD is observed when σm coincided with σc. The findings suggest that the creep rate-controlling process changes from recovery control (n=4.9) to glide control (n=3.0) below σc. These results agree well with those of conventional uniaxial creep tests. Consequently, the indentation testing technique can be used effectively to extract creep parameters from small-volume samples.

Study of the atomic structure of bcc and fcc crystals upon instantaneous plastic deformation

The evolution of the atomic structure of face-centered cubic (fcc) and body-centered cubic (bcc) crystals under the conditions of pulsed external loads and large plastic strains is investigated on the basis of computer experiments. The crystals are strained in steps to 32%. After each deformation step (2%), the system is relaxed by molecular dynamics to a new equilibrium state at 300 K. The results of the computer experiments show that plastic deformation can take place under instantaneous external loads either as a result of the motion of partial dislocations, twinning, or the turning and displacement of atomic planes, depending on the stage of the process. The laws governing the variation of the potential energy of the system and the rotation angle of the atomic planes as functions of the degree of plastic strain of the crystal are found.

Determination of the parameters of the Bodner-Partom model for thermoviscoplastic deformation of materials

UDC 539.376 The problem of describing thermoviscoplastic deformation of materials arises in modeling the behavior of structural elements under intensive loading and elevated temperature conditions, which in particular are characteristic of various industrial treatments such as welding, forging, etc. [3, 14, 18]. A rather complete review of results obtained within approaches to modeling the indicated processes is given in [5, 6]. Most of them to some degree use the concept of the yield surface and representation of the strain rate as the sum of terms corresponding to the processes of elastic and instantaneous plastic deformation and creep deformation. At the same time, it is commonly accepted that plastic deformation essentially is a time-dependent process. Attempts to develop a theory of plasticity taking into account the time and temperature dependence led to the creation of so-called unified theories. In these theories, all the characteristics of inelastic deformation are represented in a single inelastic strain term. In the evolution equation for inelastic deformation, internal variables appear whose number depends both on the hardening mechanisms (isotropic, directional) and the complexity of the loading histories under consideration. In such a formulation, the model does not explicitly contain a yield condition and related loading and unloading conditions. Thus the dependence of plastic flow on the strain rate under monotonic and cyclic loading, and also creep and stress relaxation, are determined from a single system of equations. Unified theories include those in [4, 9, 10, 15, 16]. The results of experimental study of these theories for the case of a uniaxial stress state are presented in [2, 8, 10]. It has been established that the given theories describe well the substantially nonlinear, temperature-dependent behavior of metals under complex thermomechanical loading. References [13, 19] are devoted to generalization to the case of multiaxial states. A number of papers are also available which make it possible to give a positive empirical evaluation based on comparison of finite-element calculations using the indicated models and the experimental data in problems of stress concentration and crack propagation [17], and also residual weld stresses [18]. Comparison of the major models in this class [2] shows that quantitatively and qualitatively, the thermoviscoplastic behavior of metals is described most exactly by the Bodner-Partom model [10, 11]. The paper [8] is devoted to development of a flow chart for determining the parameters of this model. In approaching this problem, we should bear in mind two facts reflecting the specifics of the model: first of all, the responsibility for the characteristic aspects of the inelastic behavior, such as the yield stress and directly several parameters of the model; secondly, the sensitivity of the model to the quality of the experimental data and the values of a number of its parameters. From this standpoint, the flow chart proposed in [8] involves assumptions and procedures (in particular, the procedure for differentiation of the experimentally obtained so-called ~,-curves) lead~g to errors in determination of the model parameters. In this paper, we develop a correct procedure for determining the desired parameters of the Bodner-Partom theory of thermoviscoplasticity, which we illustrate using the example of the AMG-6 aluminum alloy. 1. Equations of the Bodner-Partom Model. The system of constitutive equations for the Bodner-Partom model

Effect of Surface Asperity on Interfacial Contact Process Controlled by Power Law Creep—Numerical Study of Viscoplastic Adhering Process

An interfacial contact process due to power law creep is studied using a finite element technique. The contact process is assumed to be produced by power law creep alone after initial intimate contact by instantaneous plastic deformation, i.e., no diffusional mechanisms for void shrinkage are taken into account. Also, the surface oxide film is not considered. If the bonded material is deformed, then the deformation is influenced by the initial faying surface wauiness with the asperity angle αo, and the contact process is achieved by two modes; surface folding at the bond-interface (type I) and interfacial expansion (type II), where the surface folding is the phenomenon that two faying surfaces are overlapped to each other. The surface folding phenomenon occurs preferentially when αo is less than 30 deg (as the surface wauiness height decreases). On the other hand, the interfacial expansion is dominant at αo &gt; 45 deg. This can be explained in terms of the distribution of equivalent strain (stress) in the vicinity of the bond-interface.

The three processes of brittle crystalline rock creep

Three elementary processes (elastic, plastic and dilatant deformations) in brittle rock under sustained load are considered. Though these occur independently and in parallel with each other, their contributions to the creep strain of brittle rock are not equal and vary with the stages of creep. The elastic creep governs the primary stage; whereas, visco-plastic flow dominates at the secondary stage; and the third stage; i.e. the accelarating creep, is associated with the dilatant strain caused by the process of microfracturing. Besides these, the instantaneous strain at the moment of loading plays a significant role too. The strain is a function of the magnitude of the load. When the latter approaches the failure level, the instantaneous strain is a sum of the elastic deformation and instantaneous plastic deformation as well. A rheological model of such a strain is described in the paper. The primary creep duration is estimated to be three times the relaxation time of the Kelvin substances modelling elastic creep. An analysis of experimental creep curves indicates that the relaxation time for the same rock is not constant and depends upon the magnitude of the sustained load, increasing with it, via a power function. The boundary time between the secondary and tertiary creep is found from the intensity of the process of brittle rock microfracturing. A rheological model as a massive dash-pot is proposed for visualizing the accelerating creep. A method of decomposing experimental creep curves is developed to facilitate the estimation of the essential parameters of creep of the rock under testing. This allows one to design a creep curve for the same rock at an arbitrary magnitude of sustained load up to the moment of failure.

Modeling of Viscoplastic Adhering Process by a Finite Element Technique

The intimate contacting of rough surfaces in the solid state bonding of metals is modeled by a finite element method. The finite element method can be applied to the large deformation process of rate sensitive materials. The material used is an oxygen free copper. We treat only the case that the intimate contact is the rate controlling step in the solid state adhering process which can be realized under high vacuum and high temperature conditions for copper at least. The intimate contacting process is assumed to be produced by viscoplastic deformation after the initial local contact is made by instantaneous plastic deformation. The calculated results are in good agreement with the experimental ones. The model can predict the interfacial deformation during the solid state bonding carried out under high pressure conditions.

Creep deformation and creep-rupture behavior of Cr-Mo-V steel forgings.

In order to investigate creep deformation and the fracture mechanism of Cr-Mo-V steel, creep tests up to 104 h were carried out in a temperature range of 550-675°C. Metallographic observations were also conducted on the fractured specimens.The results obtained are summarized as follows:(1) Stress dependence of steady-state strain rate changes at a certain stress level, at all the temperatures studied. The stress levels of the transition in creep rate are close to those in fracture mode from transgranular to intergranular.(2) The stress level at which instantaneous plastic deformation starts (regarded as the Orowan stress), is estimated to be σ/E=1.5-2.0×10-3. This Orowan stress corresponds with the transition stress described in (1).(3) Above the Orowan stress, creep occurs mainly by the motion of dislocations within grains, which is controlled by the Orowan-bowing mechanism. In this stress range, creep rupture ductility is high.(4) Below the Orowan stress, dislocations slowly climb over particles. Because of the slow deformation within grains, the contribution of intergranular sliding increases. This results in a greater chance of intergranular cavitation, and consequently, results in a low creep rupture ductility.

Cr-Mo-V鍛鋼のクリープ変形とクリープ破断特性

In order to investigate creep deformation and the fracture mechanism of Cr-Mo-V steel, creep tests up to 104 h were carried out in a temperature range of 550-675°C. Metallographic observations were also conducted on the fractured specimens.The results obtained are summarized as follows:(1) Stress dependence of steady-state strain rate changes at a certain stress level, at all the temperatures studied. The stress levels of the transition in creep rate are close to those in fracture mode from transgranular to intergranular.(2) The stress level at which instantaneous plastic deformation starts (regarded as the Orowan stress), is estimated to be σ/E=1.5-2.0×10-3. This Orowan stress corresponds with the transition stress described in (1).(3) Above the Orowan stress, creep occurs mainly by the motion of dislocations within grains, which is controlled by the Orowan-bowing mechanism. In this stress range, creep rupture ductility is high.(4) Below the Orowan stress, dislocations slowly climb over particles. Because of the slow deformation within grains, the contribution of intergranular sliding increases. This results in a greater chance of intergranular cavitation, and consequently, results in a low creep rupture ductility.

The Mechanical Behavior of Isolated Avena Coleoptile Walls Subjected to Constant Stress

In order to assess the role of the mechanical properties of the wall in auxin-induced cell elongation, a study has been made of the ability of isolated Avena coleoptile walls to extend (creep) when subjected to a constant applied stress. Creep occurs as a viscoelastic extension which has the following characteristics: the extension is proportional to log time and is partly reversible, and the extension rate has a Q(10) of about 1.05 and is markedly greater in auxin-pretreated walls. In nonconditioned walls the extension rate is proportional to applied stress, but pre-extension causes the appearance of an apparent yield strain. The similarity of creep and instantaneous plastic deformation in response to temperature or to pretreatment with auxin or KCN suggests that the instantaneous deformation is simply the viscoelastic extension which occurs at very short times. A comparison of these viscoelastic properties with the properties of auxin-induced cell elongation indicates that cell elongation requires more than just a physical extension of the wall. It is suggested that elongation occurs as a series of extension steps, each of which involves a viscoelastic extension preceded or accompanied by an auxin-dependent biochemical change in the wall properties.