Plastic Dilatancy Research Articles

Development of an elasto-plastic constitutive model for intact rocks

A constitutive model was developed to describe the nonlinear behaviour of intact rocks under static loading. The model includes the pre-peak elastic and the post-peak strain-softening behaviour, as well as dilation. The model employs the shrinking of the failure criteria by progress of plastic deformation, to consider the strain-softening behaviour of rocks. A non-associated plastic potential function based on the dilation angle is employed to formulate the plastic deformation and dilation of rocks. Triaxial laboratory test results are used to derive the model equations. The model employs the assumptions that crack propagation in rocks during post-peak deformation is a cohesion-losing process, during which the frictional angle is constant. The assumptions were verified through careful study of the laboratory test results. In the developed model, the dilation angle is associated with the confining stress, friction angle of rocks and uniaxial compressive strength of rocks. Rocks have peak dilation angle at the point of peak strength and after that, it decreases with progress of plastic deformation, and is close to zero when rocks reach residual strength. The developed model is implemented in a finite difference code. The numerical results are compared with the test results, which show that the model captures the post-peak behaviour of rocks well.

Interpretation of Microstructural Effects on Porosity Evolution Using a Combined Dilatational/Crystal Plasticity Computational Approach

A novel formulation based on fast Fourier transforms for the prediction of ductile damage of polycrystalline materials that combines crystal plasticity and dilatational plasticity is reviewed and applied to understand the microstructural origin of available experimental evidence of porosity evolution in incipiently spalled Cu polycrystals. The influence of the Taylor factor of the crystalline ligaments linking interacting voids and the microstructural origin of a nonmonotonic grain-size dependence on porosity evolution is investigated and rationalized by means of numerical simulations using the new model.

Multiscale modeling of cohesive geomaterials with a polycrystalline approach

The main objective of this paper is to investigate the macroscopic elastic–plastic behaviors of a class of cohesive geomaterials with the aid of classical polycrystalline schemes. Specific local constitutive equations are proposed to describe the typical features of geomaterials. The local yield criterion for crystallographic sliding systems takes into account the pressure sensitivity and a non-associated plastic potential is introduced to properly describe the plastic dilatancy. Consequently, the concentration law is also modified in order to establish the relationship between the macroscopic stress tensor and the local stress tensor in each mineral grain. Computational aspects associated with the numerical implementation of polycrystalline model are revisited and discussed. The proposed model is applied to a typical polycrystalline rock, granite. After the identification of material parameters, its validity is verified through comparisons between model’s predictions and experimental data on both conventional and true triaxial compression tests.

Randomized Trial of Conventional Transseptal Needle Versus Radiofrequency Energy Needle Puncture for Left Atrial Access (the TRAVERSE‐LA Study)

BackgroundTransseptal puncture is a critical step in achieving left atrial (LA) access for a variety of cardiac procedures. Although the mechanical Brockenbrough needle has historically been used for this procedure, a needle employing radiofrequency (RF) energy has more recently been approved for clinical use. We sought to investigate the comparative effectiveness of an RF versus conventional needle for transseptal LA access.Methods and ResultsIn this prospective, single‐blinded, controlled trial, 72 patients were randomized in a 1:1 fashion to an RF versus conventional (BRK‐1) transseptal needle. In an intention‐to‐treat analysis, the primary outcome was time required for transseptal LA access. Secondary outcomes included failure of the assigned needle, visible plastic dilator shavings from needle introduction, and any procedural complication. The median transseptal puncture time was 68% shorter using the RF needle compared with the conventional needle (2.3 minutes [interquartile range {IQR}, 1.7 to 3.8 minutes] versus 7.3 minutes [IQR, 2.7 to 14.1 minutes], P=0.005). Failure to achieve transseptal LA access with the assigned needle was less common using the RF versus conventional needle (0/36 [0%] versus 10/36 [27.8%], P<0.001). Plastic shavings were grossly visible after needle advancement through the dilator and sheath in 0 (0%) RF needle cases and 12 (33.3%) conventional needle cases (P<0.001). There were no differences in procedural complications (1/36 [2.8%] versus 1/36 [2.8%]).ConclusionsUse of an RF needle resulted in shorter time to transseptal LA access, less failure in achieving transseptal LA access, and fewer visible plastic shavings.Clinical Trial RegistrationURL: http://www.clinicaltrials.gov. Unique identifier: NCT01209260.

Modeling void growth in polycrystalline materials

Most structural materials are polycrystalline aggregates whose constituent crystals are irregular in shape, have anisotropic mechanical properties and contain a variety of defects, resulting in very complicated damage evolution. Failure models of these materials remain empirically calibrated due to the lack of a thorough understanding of the controlling processes at the scale of the materials’ heterogeneity, i.e. the mesoscale. This paper describes a novel formulation for a quantitative, microstructure-sensitive three-dimensional mesoscale prediction of ductile damage of polycrystalline materials, in the important void growth phase of the process. Specifically, we have extended a formulation based on fast Fourier transforms to compute growth of intergranular voids in porous polycrystalline materials. In this way, two widely used micromechanical formulations, i.e. polycrystal plasticity and dilatational plasticity, have been efficiently combined, with crystals and voids represented explicitly, to predict porosity evolution. The proposed void growth algorithm is first validated by comparison with corresponding finite-element unit cell results. Next, in order to isolate the influence of microstructure on void growth, the extended formulation is applied to a face-centered cubic polycrystal with uniform texture and intergranular cavities, and to a porous material with homogenous isotropic matrix and identical initial porosity distribution. These simulations allow us to assess the effect of the matrix’s polycrystallinity on porosity evolution. Microstructural effects, such as the influence of the Taylor factor of the crystalline ligaments linking interacting voids, were predicted and qualitatively confirmed by post-shocked microstrostructural characterization of polycrystalline copper.

Experimental Investigations into the Mechanical Behaviour of the Breccias Around the Proposed Gibraltar Strait Tunnel

The proposed Gibraltar Strait tunnel will cross two zones with breccia consisting of a chaotic mixture of blocks and stones embedded in a clay matrix. The breccia is saturated, has a high porosity and exhibits poor mechanical properties in the range between hard soils and weak rocks. The overburden and high in situ pore pressures in combination with the low strength of the breccia may lead to heavy squeezing. The crossing of the breccia zones thus represents one of the key challenges in the construction of the tunnel. In order to improve our understanding of the mechanical behaviour of the breccias, a series of triaxial compressions tests were carried out. Standard rock mechanics test equipment was not adequate for this purpose, because it does not provide pore pressure control, which is important in the case of saturated porous materials. Pore pressure control is routine in soil mechanics tests, but standard soil mechanics equipment allows only for relatively low nominal loads and pressures. In addition, the low hydraulic conductivity of the breccias demands extremely low loading rates and a long test duration. For these reasons, we re-designed several components of the test apparatus to investigate the mechanical behaviour of the breccia by means of consolidated drained and undrained tests. The tests provided important results concerning the strength, volumetric behaviour, consolidation state and hydraulic conductivity of the breccias. The present paper describes the test equipment and procedures, provides an overview of the test results and discusses features of the mechanical behaviour of the breccias which make them qualitatively different from other weak rocks such as kakirites—a typical squeezing rock in alpine tunnelling. The paper also demonstrates the practical importance of the experimental findings for tunnelling in general. More specifically, it investigates the short-term ground response to tunnel excavation from the perspective of elasto-plastic behaviour with the Mohr–Coulomb yield criterion. The computational results indicate that the breccias will probably experience very large deformations already around the advancing tunnel heading, which can be reduced considerably, however, by advance drainage. The analyses additionally show that plastic dilatancy is favourable with respect to the short-term response, thus highlighting the importance of the constitutive model when it comes to theoretical predictions.

Mechanical Properties and Tensile Deformation Behavior of Polyamide 6/Maleated and Unmaleated Ethylene Propylene Diene Terpolymer/Nano-CaCO3 Ternary Composites

Ternary composites composed of polyamide 6 (PA6), a mixture of maleated (EPDM-g-MA) with unmaleated ethylene propylene diene terpolymer (EPDM) rubber at weight ratio 80/20 (defined as EPDM-M), and nano-calcium carbonate (nano-CaCO3) were prepared by a two-step compounding route. Sandbag microstructure, in which nano-CaCO3 agglomerates were embedded EPDM-M, were observed by scanning electron microscopy (SEM). Deformation of the composites was studied by video-aided tensile tests during uniaxial tension. The microstructural morphology and interfacial interaction were investigated through SEM and dynamic mechanical analysis (DMA). Compared to PA6/EPDM-M/nano-CaCO3 ternary composites without sandbag microstructure (E2), the microstructural morphology of PA6/EPDM-M/nano-CaCO3 ternary composites with sandbag microstructure (E3) showed that numerous microfibrils and cavitations were formed by simultaneously stretching and debonding of nano-CaCO3 agglomerates and EPDM-M in the sandbag microstructure, which resulted in a higher volume strain and larger quantity of energy dissipation. Additionally, better interfacial interaction between the sandbag microstructure and PA6 matrix in E3 caused a lower α-relaxation temperature and easier external energy transmission than E2 without sandbag microstructure. Consequently, the presence of the sandbag particles in PA6/EPDM-M/nano-CaCO3 ternary composites changed the tensile yield deformation of PA6 from a more deviatoric plasticity to a more dilatational plasticity.

Constitutive equations of a tensorial model for ductile damage of metals

Based on a micromechanical concept of void growth and change in void shape, a dissipation potential and constitutive equations for ductile damage of metals are presented. Multiplicative decomposition of the metric transformation tensor and thermodynamic formulation of the constitutive equations lead to a symmetric second-order tensor of damage which is physically meaningful. Its first invariant defines the damage related to plastic dilatation of the material due to the void growth. The second invariant of the deviatoric tensor accounts for the damage associated with a change in the void shape. Two physically motivated normalized measures allow us to represent the kinetic process of strain-induced damage by using the equivalent parameter of damage including the limit conditions for the onset of void coalescence and ductile failure. An experimental analysis of the evolution of ductile damage is presented for the case of uniaxial tension of sheet steel specimens with artificial defects.

Effect of single-crystal plastic deformation mechanisms on the dilatational plastic response of porous polycrystals

In this paper, the combined effects of texture and asymmetric single-crystal plastic deformation mechanisms on the dilatational response of voided polycrystals are assessed for the first time. To this end, a full-field dilatational viscoplastic Fast Fourier Transform (FFT)-based approach is used to generate gauge surfaces for porous polycrystals deforming by twinning at single crystal level, which are compared to yield surfaces obtained according to a recent analytical criterion for porous materials. Both approaches are cross-validated, revealing unusual features of the dilatational response, namely, a lack of symmetry of the surfaces with respect to both the hydrostatic and deviatoric axes. This strong sensitivity to the third invariant of the stress deviator is associated to the anisotropy and the tension–compression asymmetry of the plastic response of the matrix.

Numerical simulation of low-velocity impact loading of a ductile polymer material

Mechanical impact loading of injection-moulded components was simulated. The material was a talc-filled and elastomer-modified polypropylene used in automotive exterior parts. The material model was the linear-elastic–viscoplastic SAMP-1 model, which features pressure-dependent yield stress, plastic dilatation and a simple damage model. The model was calibrated with data from tests in uniaxial tension, shear and uniaxial compression, utilising 3D digital image correlation for full-field displacement measurements. With the calibrated model, two load cases were simulated; centrally loaded clamped plates and three-point bending of bars. The predictions of force vs. deflection were good to fair. The results are discussed in terms of deficiencies of the calibration data, heterogeneity and anisotropy of injection-moulded components, and shortcomings of the model. In particular, the hardening curves at high strain rates are uncertain, and tests in biaxial tension would be useful.

A combined experimental–numerical investigation of ductile fracture in bending of a class of ferritic–martensitic steel

We present a combined experimental–numerical study on fracture initiation at the convex surface and its propagation during bending of a class of ferritic–martensitic steel. On the experimental side, so-called free bending experiments are conducted on DP1000 steel sheets until fracture, realizing optical and scanning electron microscopy analyses on the post mortem specimens for fracture characterization. A blended Mode I – Mode II fracture pattern, which is driven by cavitation at non-metallic inclusions as well as martensitic islands and resultant softening-based intense strain localization, is observed. Phenomena like crack zig-zagging and crack alternation at the bend apex along the bending axis are introduced and discussed. On the numerical side, based on this physical motivation, the process is simulated in 2D plane strain and 3D, using Gurson’s dilatant plasticity model with a recent shear modification, strain-based void nucleation, and coalescence effects. The effect of certain material parameters (initial porosity, damage at coalescence and failure, shear modification term, etc.), plane strain constraint and mesh size on the localization and the fracture behavior are investigated in detail.

The Mechanical Properties of Epoxy Composites Filled with Rubbery Copolymer Grafted SiO2

This study demonstrated a method for toughening a highly crosslinked anhydride cured DGEBA epoxy using rubbery block copolymer grafted SiO2 nanoparticles. The particles were synthesized by a sequential reversible addition-fragmentation chain transfer (RAFT) polymerization. The inner rubbery block poly(n-hexyl methacrylate) (PHMA) had a glass transition temperature below room temperature. The outer block poly(glycidyl methacrylate) (PGMA) was matrix compatible. A rubbery interlayer thickness of 100% and 200% of the particle core radius was achieved by grafting a 20 kg/mol and a 40 kg/mol PHMA at a graft density of 0.7 chains/nm2 from the SiO2 surface. The 20 kg/mol rubbery interlayer transferred load more efficiently to the SiO2 cores than the 40 kg/mol rubbery interlayer and maintained the epoxy modulus up to a loading of 10 vol% of the rubbery interlayer. Both systems enabled cavitation or plastic dilatation. Improvement of the strain-to-break and the tensile toughness was found in both systems. We hypothesize that plastic void growth in the matrix is the primary mechanism causing the improvement of the ductility.

Modeling microstructural effects in dilatational plasticity of polycrystalline materials

In a recent paper [1] we presented a new constitutive model for the viscoplastic response of polycrystalline aggregates accounting for local anisotropy induced by crystal plasticity and dilatational effects associated with the presence of intergranular cavities. In this contribution we provide a summary of our findings, as well as previously unpublished details of the numerical algorithm underlying this novel formulation. The formulation is based on homogenization and captures microstructural effects on the dilatational plastic behavior of polycrystalline materials. These effects are relevant to many engineering problems in which the presence of cavities embedded in a heterogeneous and anisotropic polycrystalline matrix must be accounted for, and for which standard polycrystalline models of incompressible plasticity, or dilatational plasticity formulations for voided materials with uniform properties of the matrix, have been proven to be insufficient. The present approach makes use of variational linear-comparison homogenization methods to develop constitutive models simultaneously accounting for texture of the matrix, porosity and average pore shape and orientation. The predictions of the models are compared with full-field numerical simulations based on fast Fourier transforms to study the influence of different microstructural features (e.g. overall porosity, single-crystal anisotropy, etc.) and triaxiality on the dilatational viscoplastic behavior of voided fcc polycrystals.

A coupled elasto-plastic-damage mechanical model for marble

A profound understanding of the mechanical behaviors of marble is very important for the design and construction of deep diversion tunnels in Jinping II hydropower station. In this paper, a coupled elasto-plastic-damage mechanical model is presented for Jinping marble. Firstly, the experimental investigations on Jinping marble are summarized. Then, based on the framework of continuum damage and plastic theories, a general mechanical model is proposed to predict the mechanical responses of Jinping marble. The proposed model is used to simulate the triaxial compressive tests, and there is a general good agreement between experimental data and numerical predictions in a qualitative manner. The proposed model is able to capture the main features of Jinping marble observed in experiments, such as progressive yielding process, damage induced by plastic distortion, dilation, elastic degradation and stress sensitivity.

Identification of material parameters for Drucker–Prager plasticity model for FRP confined circular concrete columns

Existing research works have established that Drucker–Prager (DP) plasticity model is capable of modeling stress–strain behavior of confined concrete. However, accuracy of the model largely depends on adequate evaluation of its parameters that determine the yield criterion, hardening/softening rule and flow rule. Through careful analytical studies of test results of FRP confined concrete columns under theoretical framework of the DP model, it is found that: (1) the hardening/softening rule is governed by plastic strains and the FRP stiffness ratio; (2) the friction angle decreases slightly with an increase in plastic deformation; and (3) the plastic dilation angle is a function of both axial plastic strain and the FRP stiffness ratio. Explicit models for these properties are developed from analytical studies. By implementing the proposed models in ABAQUS, finite element analyses can well predict stress–strain responses of FRP confined concrete columns.

Application of Drucker-Prager Plasticity Model for Stress-Strain Modeling of FRP Confined Concrete Columns

Existing research works have identified that Drucker-Prager (DP) plasticity model is capable of modeling the stressstrain behavior of confined concrete. However, the accuracy of the model largely depends on the adequate evaluation of its parameters that determine the yield criterion, hardening/softening rule and flow rule. Up to date, most research works mainly focus on the first two criteria. The plastic dilation angle is the major parameter that governs the DP flow rule. This paper addresses the plastic dilation properties of concrete for FRP confined circular concrete columns under the theoretical framework of DP model in the commercial software ABAQUS. Through careful analyses of test results for FRP confined concrete columns, it is found that the plastic dilation angle is a function of axial plastic strain and the lateral stiffness ratio. A simple model for the plastic dilation angle is subsequently developed. With the implementation of this model, the finite element analysis results fit well with the experimental stress-strain curves for columns with both low and high confinement.

Surgical treatment of biliary ductal stricture complicating localized left hepatolithiasis.

To summarize the experience in the clinical treatment of biliary duct strictures complicating localized left hepatolithiasis in the last two decades. A retrospective analysis of 67 cases of biliary duct strictures complicating localized left hepatolithiasis treated in our center in the last two decades was made with regards to each patient's age, gender, results of various preoperative examinations, operative findings, treatment and postoperative courses. The incidence of left hepatic duct (LHD) stricture was 59.8% and that of a left external hepatic duct (LEHD) stricture was 84.0 % and 84.8% respectively, in which a severe degree dominated. Among the operative procedures used in the treatment of LHD strictures, plastic operation plus biliary enteric anastomosis ranks first in frequency (52.2%), with a re-stricture rate of 17.1%. Left lobectomy ranks third (19.4%) with no re-stricture. Simple plastic performance or dilation had a high occurrence rate of re-stricture and usually needed subsequent surgery. Most LEHD strictures were eradicated by lateral segmentectomy or lobectomy, whereas most LMHD strictures were just the opposite. The rate of preoperative diagnosis of LMHD by endoscopic retrograde cholangiography, percutaneous transhepatic cholangiography, computed tomography or intraoperative and postoperative trans-T-tube cholangiography was much lower than that of LEHD or extrahepatic duct. Too much attention paid to LEHD disorders in the treatment of localized left hepatolithiasis potentially results in negligence or omission in LMHD disorders. Malpractice treatments of LHD strictures are important factors affecting the long term results of localized left hepatolithiasis, for which left lobectomy is usually the therapy of choice.

An out-of-plane length scale for ductile crack extensions in 3-D SSY models for X65 pipeline materials

This paper investigates the ductile crack extension in the API 5L X65 pipeline steels in 3-D small-scale yielding (SSY) models using the Gurson-Tvergaard (GT) dilatational plasticity model implemented in the “computational cell” framework. The objective of the study targets at determining an out-of-plane length scale of the computational cell for 3-D crack extensions in fracture models with a through-thickness, straight crack front. The basic Gurson material parameters: the initial void volume fraction f0 and the in-plane size of the computational cell D, calibrate from a set of notched tension specimens fabricated using API X65 steels. Cell extinctions based on a critical void volume fraction facilitates the process of the void growth and void coalescence which leads to the final failure of the “cell” and thus crack extensions. This study examines two types of 3-D SSY models: the side-grooved model and the plane-sided model. The element size in the thickness direction imposes significant effects on the computed fracture resistance and crack extension. Converged predictions of the J-Δa curve requires the out-of-plane length scale near the side groove equal to the in-plane length scale D. Plane-sided models converge faster than does the side-grooved model and requires the out-of-plane length scale to be 2D near the free surface. The required out-of-plane length scale does not indicate strong dependence on the material hardening exponent and the initial void volume fraction of the material.

Some applications of Burzyński yield condition in metal plasticity

The classical J 2 plasticity theory is widely used to describe the plastic response of metallic materials. However, this theory does not provide satisfactory predictions for materials which exhibit pressure-sensitive yielding or plastic dilatancy. Another difficulty is the difference between the values of yield stresses in tension and compression for isotropic materials, the so-called strength differential effect (SD), leading to the asymmetry of the elastic range. The Burzyński yield condition, proposed in 1928, can be used to overcome some of these problems. In this paper an implicit integration of the elasto-plastic constitutive equations for the paraboloid case of Burzyński’s yield condition is formulated. Also, the tangent operator consistent with the integration algorithm was developed and is presented. The proposed model was implemented in a commercial Finite Element code and different kinds of tests reported in the literature were simulated. The comparison between the numerical and experimental results shows that the plasticity theory with the paraboloid case of Burzyński’s yield condition describes adequately the strength differential effect, which is present in many kinds of materials significant for recent applications.

Experimental study and modeling of damage of Al alloys using tensor theory

This article presents and evaluates experiments for the characterization and modeling of damage of structural aluminum and aluminum–magnesium alloys. Tensile tests were performed for specimens with artificial defects (voids) represented by different arrangements of pre-drilled micro-holes. The corresponding stress–strain curves were experimentally obtained. Plastic dilatation and deviatoric strain were determined both for the local zones with artificial defects and directly for meso-elements (i.e., material cells with artificial defects). A symmetric second-rank order tensor of damage was applied for a quantitative estimate of the material damage connected with the volume fraction and shape of micro-defects. The definition of this tensor is physically motivated, since its hydrostatic and deviatoric parts describe the evolution of damage connected with a change in volume fraction and shape of micro-defects, respectively. Such a representation of damage kinetics allows us to use two integral measures for the calculation of damage in deformed materials. The first measure determines damage related to an increase in void volume fraction (i.e., plastic dilatation). A critical amount of plastic dilatation corresponds to the moment of macro-fracture of the deformed metal. By means of experimental analysis, we can determine the function of plastic dilatation which depends on the strain accumulated by material particles under various stress and temperature-rate conditions of forming. The second measure accounts for the deviatoric strain of meso-elements, and is related to the change in their shapes. The critical deformation of ellipsoidal voids corresponds to the onset of their coalescence and to the formation of large cavernous defects. The second measure is considered as a criterion of micro-destruction due to formation of cavities in the deformed material. Based on the experimental data, some numerical modeling is realized for the investigated Al alloys to taken a change in stress triaxiality into account. It shows that a change in triaxiality toward smaller values results in an appreciable decrease of damage induced by strain. Both damage measures are important for the prediction of the meso-structure quality of metalware produced by metal forming techniques.