Inelastic Volume Change Research Articles

Experimental study on the effective measurement of the total homogenization temperature of high internal pressure CO<sub>2</sub>-rich fluid inclusions in orogenic gold deposits: A case study of the Yufeng gold deposit, Eastern Tianshan Orogen

形成于中-深成条件下的造山型金矿的成矿流体属于H₂O-NaCl-CO₂体系，金矿化阶段的石英中发育大量的富CO₂流体包裹体。长期以来，用常规冷热台对其进行显微测温热力学研究时，较高的内压力会造成绝大多数CO₂充填度>0.4的包裹体在尚未达到完全均一状态前就发生爆裂或泄露，导致所测的完全均一温度值明显偏离真实值，甚至无法测得完全均一温度，这制约了对造山型金矿床成矿条件的认知。针对该问题，本文以东天山玉峰金矿床富金矿石中的H₂O-NaCl包裹体（A型）和H₂O-NaCl-CO₂包裹体（AC型）为研究对象，介绍了利用最新型热液金刚石压腔（HDAC-VT型号）测试富CO₂高内压的AC型包裹体完全均一温度的实验流程与结果，并将实验数据与Linkam THMSG600冷热台测得的A型、AC型包裹体的完全均一温度进行了对比分析。实验结果表明，热液金刚石压腔能够有效阻止富CO₂流体包裹体在升温过程中发生爆裂、泄露等非弹性体积改变现象的发生，从而获得有效的完全均一温度。同时，本文还提出了一个新的压力-温度拟合线两线相交法，对热液金刚石压腔所测富CO₂流体包裹体的完全均一温度数据进行校正，以最大程度上减少外压力造成的影响，获得更为接近真实成矿流体的完全均一温度。基于此，获得玉峰金矿床的成矿温度和成矿压力分别为312~343℃和181~268 MPa。本文的实验研究工作显示了热液金刚石压腔在中-深成造山型金矿富CO₂成矿流体的研究领域具有重要应用前景。;The ore-forming fluids of orogenic gold deposits normally belong to a H₂O-NaCl-CO₂ system, and there are usually lots of CO₂-rich fluid inclusions hosted in the quartz at the gold mineralization stage. The trapped fluid inclusions in this type of gold deposit usually have high internal pressures since they are formed at a mid-deep depth in the earth's crust. For a long time, almost all researchers carry out the homogeneous thermomechanical properties study on CO₂-rich inclusions (CO₂ phase filling ratio>0.4) under a 1atm pressure condition. However, when the internal pressure is greater than the external confining pressure, the fluid inclusion will be deformed, such as stretching, leakage and decrepitating, which eventually lead to the measured total homogenization temperature (THT) deviate significantly from the actual value, or even cannot be measured. In order to solve these problems, we choose H₂O-NaCl (A-type) and H₂O-NaCl-CO₂ (AC-type) inclusions in quartz minerals from Yufeng orogenic gold deposit in Eastern Tianshan Orogen as the research object to measure their THTs with high internal pressures by using the latest hydrothermal diamond-anvil cell (HDAC; HDAC-VT type). At the same time, this manuscript compares the THTs obtained by a HDAC-VT with those by a Linkam THMSG600 heating-freezing stage. Our experimental results show that the HDAC can effectively prevent the inelastic volume change of CO₂-rich fluid inclusions during heating process, and consequently obtain an effective THT. In order to minimize the influence of external pressure on the measured THTs and obtain more reliable and accurate metallogenic temperatures, we propose a new two pressure-temperature fitting lines intersection method to calibrate the THTs of CO₂-rich fluid inclusions measured by a HDAC. Based on these improvements, the ore-forming temperatures and pressures of the Yufeng gold deposit are estimated to be 312~343℃ and 181~268MPa, respectively. The experimental work in this paper suggests that the HDAC has an important application prospect in the research field of CO₂-rich fluid inclusions from orogenic gold deposits.

Is crystal plasticity non-conservative? Lessons from large deformation continuum dislocation theory

Crystal plasticity for large plastic deformations is usually modeled as volume conserving. However, there is experimental evidence that huge amounts of vacancies are produced during plastic deformation. The only regularly considered mechanism of non-conservative dislocation motion is climb of edge dislocations, but this is supposed to be enabled by high vacancy concentrations rather than producing them. In the current contribution we show that large deformation kinematics applied to evolving fields of geometrically necessary dislocations accounts for kinking and jogging of dislocations when cutting through one another. Therefore, dislocation fields in multiple slip situations will not be confined to slip planes and their motion will necessarily involve non-conservative motion of jogs. Because inelastic volume changes in crystals are only possible in the presence of point defects, we find that large deformation continuum dislocation theory must be coupled to an evolving vacancy concentration. We suggest to treat vacancy diffusion as an independent inelastic deformation mechanism yielding a three-way multiplicative decomposition of the deformation gradient. Small numerical examples are used to illustrate the kinematics of emerging and moving kinks and jogs, and the ensuing production of vacancy concentration. Continuum thermodynamics is used to derive coupled evolution equations for geometrically necessary dislocation density vectors and vacancy concentration. We conclude that large deformation crystal plasticity as an averaged theory of dislocations may not be conservative and that the usual kinematic assumption Lp=∑sγ˙sms⊗ns does not hold in multiple slip deformation.

A phenomenological model for the inelastic stress–strain response of a potato tuber

In this article, we synthesise concepts from the theories of plasticity, volumetric growth, and pseudo-hyperelasticity to develop a phenomenological constitutive model for potato tuber tissue. Here, particular focus is laid on the inhomogeneity of the constitutive behaviour across different anatomical zones of a potato tuber. The internal stresses are expressed in terms of an elastic contribution to the local strains and are controlled by a kinetic memory variable that traces the past strain history. Inelastic strains, by contrast, are considered as a combination of a plastic component and a pure volumetric component mimicking the eviction of fluid. Considering tubers of cultivar Belana, we identify the relevant constitutive parameters based on stress–stretch curves obtained from single-cycle uniaxial compression experiments on samples extracted from different anatomical tuber parts. The stress–strain response of the tissue is characterised by a pronounced and well-reproducible hysteresis which displays slight stiffening along the initial loading branch. Considering the parenchyma microstructure, the significant reduction in tissue turgidity on unloading may be caused by the eviction of intracellular fluid from the parenchyma cells and an inelastic cell wall response. The experiments show that the inelastic volume change varies approximately linearly with the axial stretch. Additionally, histological analyses are presented in an attempt to quantify microstructural inhomogeneities.

Anisotropic finite hyper-elastoplasticity of geomaterials with Drucker–Prager/Cap type constitutive model formulation

The formulation of large strain anisotropic hyper-elastoplasticity of geomaterials is examined. Attention is given to the role of structure tensors (also called fabric tensors), especially in context of the Eshelby–Mandel stress and large inelastic volume changes attributable to porosity. Both (hyper-)elastic and inelastic orthotropic symmetry, reducing to the particular case of transverse isotropy, are considered. Specific material assumptions and constitutive choices are identified for the development of a novel Anisotropic Drucker–Prager/Cap (ADPC) model formulated within the intermediate configuration consistent with multiplicative split of the deformation gradient. The model is calibrated to existing experimental measurements, including high pressure large strain triaxial compression of lithographic (Solnhofen) limestone and triaxial compression measurements on Tournemire shale assessing elastoplastic anisotropy. Manifest implications of constitutive theory are investigated, including consequences of recognizing (or not) the Eshelby–Mandel stress as energy conjugate to the plastic velocity gradient and including (or not) contribution from the skew-symmetric parts of the Mandel stress to the plastic anisotropy. Numerical simple shear experiments and large deformation simulated indentation experiments are provided in order to investigate model predictions and demonstrate the overall robustness in finite element modeling.

Nonlinear thermomechanics for analysis of weak shock profile data in ductile polycrystals

Modeling of shock compression of isotropic, polycrystalline elastic-plastic solids that deform by dislocation glide is undertaken. Internal energy density of the material depends on a thermoelastic Eulerian strain tensor, entropy, and an internal state variable representative of dislocation density. Dislocation glide is incompressible, but inelastic volume changes arising from residual local strain fields and core effects of dislocations are captured. A semi-analytical method is advanced for extracting inelastic constitutive response information from particle velocity histories of polycrystalline samples under planar shock loading. The only parameters entering the procedure are fundamental thermoelastic properties and assumed bounds on the fraction of plastic work corresponding to energy storage of generated dislocations in the lattice. Densities of statistically stored and geometrically necessary dislocations, in addition to shear stress, plastic strain, plastic strain rate, and temperature, are outcomes of the analysis. The model is implemented for polycrystalline aluminum and copper. Certain results are compared with others in the literature obtained under different kinematic and thermodynamic assumptions. Effects of choices of nonlinear thermoelastic formulations and higher-order elastic constants on extracted deviatoric stress profiles can be substantial. Stored energy of dislocations and commensurate residual volume changes together can notably affect extracted shear stress. Stored energy significantly affects predicted entropy production and its contribution to temperature rise. The calculated density of geometrically necessary dislocations required to maintain compatibility of total strain across the structured steady plastic wave front is small relative to the line density of total dislocations.

Dilatancy as a measure of fracturing development in the process of rock damage

Abstract Dilatancy understood as inelastic volume changes of rock under conditions of differential stress not only foreshadows brittle rock failure [1, 2, 3], preceding such phenomena as earthquakes or mining-induced rockbursts, but also defines the kinematics of rock deformation [4, 5]. This article shows that there is a quantitative relationship between the dilatancy occurring at different levels of rock load and the development of fracturing that accompanies the process of rock degradation. Based on the mechanical laboratory test results of Wustenzelleer fine-grained sandstone, the article presents analyses of plastic volume changes in rock samples and a certain measure of fracture development accompanying the process of their degradation. Thanks to the characteristics obtained through mechanical tests with unloading, the inelastic volumetric strain of the samples was established, and the scalar damage variable (CDM - continuum damage mechanics approach) was determined at various load levels. These results demonstrated the relationship between dilatancy and rock stiffness changes describing the development of fracturing. Three load intervals were determined, in which the nature of the analysed phenomena, i.e. dilatancy and damage describing the development of cracks, undergoes significant changes. The highest intensity of both phenomena was obtained in the post-critical load range, between the ultimate strength limit and the residual strength of the samples, in which rock samples undergo the process of degradation the most. Obtained dependencies allow the correlation to be taken into account in damage mechanics models describing the variable stiffness of rocks in the loading process.

Phase Field Theory and Analysis of Pressure-Shear Induced Amorphization and Failure in Boron Carbide Ceramic

A nonlinear continuum phase field theory is developed to describe amorphization of crystalline elastic solids under shear and/or pressure loading. An order parameter describes the local degree of crystallinity. Elastic coefficients can depend on the order parameter, inelastic volume change may accompany the transition from crystal to amorphous phase, and transitional regions parallel to bands of amorphous material are penalized by interfacial surface energy. Analytical and simple numerical solutions are obtained for an idealized isotropic version of the general theory, for an element of material subjected to compressive and/or shear loading. Solutions compare favorably with experimental evidence and atomic simulations of amorphization in boron carbide, demonstrating the tendency for structural collapse and strength loss with increasing shear deformation and superposed pressure.

Creep and Dilatancy Behavior of Rock Salt around Underground Caverns

In the present paper, the time-dependent behavior of a salt cavern was analyzed using finite element method. A viscoplastic model considering inelastic volume changes was utilized to describe the time-dependent mechanical behavior of rock salt. The model was then implemented in a finite element procedure to analyze the stress and deformation of rock salt around an underground cavern using an axisymmetric representation. Finally, finite element analyses results were compared with those obtained by a viscoplastic model neglecting inelastic volume changes.

Failure analysis of R/C columns using a triaxial concrete model

Inelastic failure analysis of concrete structures has been one of the central issues in concrete mechanics. Especially, the effect of confinement has been of great importance to capture the transition from brittle to ductile fracture of concrete under triaxial loading scenarios. Moreover, it has been a challenge to implement numerically material descriptions, which are susceptible to loss of stability and localization. In this article, a novel triaxial concrete model is presented, which captures the full spectrum of triaxial stress and strain histories in reinforced concrete structures. Thereby, inelastic dilatation is controlled by a non-associated flow rule to attain realistic predictions of inelastic volume change at various confinement levels. Different features of distributed and localized failure of the concrete model are examined under confined compression, uniaxial tension, pure shear, and simple shear. The performance at the structural level is illustrated with the example of a reinforced concrete column subjected to combined axial and transverse loading.

Fracture Energy Formulation for Inelastic Behavior of Plain Concrete

A constitutive formulation is presented that covers the triaxial load‐response spectrum of plain concrete in tension as well as in shear. The elastoplastic concrete model resorts to an isotropic‐hardening description of the prepeak behavior and to a fracture energy‐based isotropic‐softening description of the post‐peak response. To control inelastic dilatancy, a nonassociated plastic flow rule is adopted in regard to the inelastic volume change. The constitutive parameters are calibrated from a series of stroke‐controlled laboratory experiments that include the direct‐tension test and triaxial compression tests at three different levels of confinement. The predictive capabilities of the proposed model are assessed with a broad range of experimental data. The issue of failure on the constitutive level is addressed with the aid of the instability indicator for continuous material branching and the localization indicator for the formation of weak discontinuities. The relevance of these two failure diagnostic...

The Multiaxial constitutive law for concrete structures subjected to impact loading

Abstract This paper aims to provide a constitutive law for describing the rate depedent triaxial behavior of concrete subjected to impact loading. The proposed damage‐plastic loading surface model is characterized by normality, continuity, convexity and associatedness. It utilizes two loading surfaces, of which the slanted ellipse loading surface describes the behavior associated with damage due to inelastic volume change and the other plasticity of no inelastic volume change. The smeared crack model is used for analysis. The contact‐impact relation is formulated based on the law of mass conservation, the law of linear momentum and the law of conservation of energy. The proper treatments are taken to modify the coalescence condition, release condition and maintained contact condition for two impact subjects. To calibrate the material constants of this constitutive law, one only needs to know the results of the uniaxial tensile test, the uniaxial compressive test, the biaxial and triaxial compressive test ...

Damage-plastic loading surface model for concrete

The paper presents a plasticity-type model which is characterized by normality, continuity, convexity and associatedness. It utilizes two loading surfaces, of which one describes the behavior associated with damage due to inelastic volume change (expansion from micro-cracking, or contraction from pore collapse or closure) and the other plasticity at no inelastic volume change. Since only one of these two surfaces is active at the same time, the formulation is equivalent to a single loading surface. The deviatoric section of the damage loading surface is a rounded triangle, and the Rendulić section meridians have the shape of a slanted ellipse. The loading surfaces are smooth and have no corners. Although the model involves approximately the same number of material constants as the previous models of similar capability, identification of these constants from test data is much simpler. The properties of the model are also more advantageous for numerical finite element applications. The model is shown to be capable of describing the basic uniaxial and multiaxial test data for concrete except degradation of material stiffness.

Hysteretic Endochronic Theory for Sand

A new form of endochronic constitutive model is presented to describe the behavior of dry or drained sand, and its parameters are determined by extensive comparisons with published test data. Jump‐kinematic hardening is used to guarantee that the hysteresis loops always close, yield positive energy dissipation, and give an increase in tangent modulus when unloading changes to reloading. Criteria for virgin loading, unloading and reloading are formulated in terms of deviatoric work, and changes of material parameters at loading‐unloading‐reloading transition points are determined. Two endochronic units coupled in parallel are used to describe the measured response over a broad range of strain amplitude. The inelastic volume change is characterized so as to include both densification and dilatancy. Certain material properties are determined as functions of the void ratio. Calculations show that the lateral stress in a simple shear test quickly becomes almost equal to the vertical stress. A three‐dimensional finite element analysis of the simple shear test with endochronic theory reveals significant stress nonuniformity; but this is found to have little effect on the resulting hysteresis loops.

Effect of hydrostatic pressure on the deformation behavior of polyethylene and polycarbonate in tension and in compression

AbstractThe stress‐strain response of crystalline high density polyethylene and of amorphous polycarbonate has been determined in tension and in compression at superimposed pressures up to 1104 MPa(160 ksi). Strain softening occurred in the polycarbonate at low pressures but was inhibited by pressure. Tensile necking occurred in both materials, but was promoted by pressure in polyethylene and inhibited in polycarbonate. The initial modulus, E, and the flow stress, σ, at a given offset strain varied linearly with the mean pressure, P, with essentially the same pressure coefficient, α. Thus, E = (1+αP)E0 and σ = (1+αP)σ0, where E0 and σ0 are values at zero mean pressure. In polyethylene, the coefficient, σ0, was the same in tension and compression, indicating that the strength differential between tension and compression was a simple manifestation of pressure‐dependent yielding. In polycarbonate the coefficient, σ0, was different in tension and in compression, implying an effect due to the third stress invariant or to anisotropy. The results suggest a constitutive model for polymers in which the flow stress is linearly dependent on mean pressure, but in which inelastic volume change is negligible. The results also suggest that the pressure dependence of flow stress in polymers is the same as that of the initial modulus.