Nonlinear Plastic Deformation Research Articles

Design and Nonlinear Dynamic Response of a Steel Stack

AbstractIndustrial stacks are built in order to reduce atmospheric pollution and release gases to the higher level of the atmosphere. Since they are high and slender structures, they are significantly affected by lateral forces, in particular, induced by winds and earthquakes. This paper aims to summarize the design principles for steel stacks given in the international standards, codes and specifications considering the evaluation of the results from the investigation on nonlinear dynamic response of a typical steel stack subjected to the earthquake. For this purpose, a typical self-supporting steel stack has been designed and its performance under earthquake and wind forces has been investigated in terms of the applied design principles, such as the displacement limit and the potential plastic deformations. The study is accomplished by using finite element models employing nonlinear time history and pushover analyses. The numerical results are presented particularly by considering the design principles used for the model. The results show that wind loads considered are more pronounced in the design of industrial steel stacks than earthquake especially in terms of limiting top displacement. The flue openings which reduce strength and lateral stiffness of the stack web is significantly effective in the lateral behavior of the stack. Moreover, the principles considered are found applicable for the design of such steel stacks. Based on the results from nonlinear time history analyses, no yielding and plastic deformation are detected along the stack.

Modern Theory of Creep of Reinforced Concrete

The important features of the theory of creep of reinforced concrete, identified and published earlier, are explored. The creation and development of the theory of creep of reinforced concrete is based on non-scientific principles take from systems of classical mechanics that do not correspond to this theory. A detailed analysis of the theory used in many countries was performed, while five oversimplifications were identified that reject fundamental experiments, Eurocodes, rules of mathematics and mechanics: listed in the law of creep, oversimplifications that grossly distort the calculation results, not only the deformations themselves, but also subsequent methods for calculating reinforced concrete structures. These include: unnecessarily modified classical Hooke’s law; imposing a property missing from concrete - an algebraic measure of creep; erroneous superposition principle; use of viscoelastic deformations instead of instantaneous nonlinear plastic deformations; replacement of obvious - nonlinear and non-stationary properties of concrete with linear ones, distorting the qualitative side of phenomena inherent only in nonlinear systems. These errors are covered by unreasonable safety factors, which undermines the economic component of the problem, and of the enormous volumes of reinforced concrete used throughout the world, the analyzed unscientific theory of its calculation causes enormous economic damage in global construction.

Effects of Mode Mixity and Loading Rate on Fracture Behavior of Cracked Thin-Walled 304L Stainless Steel Sheets with Large Non-Linear Plastic Deformation.

This study investigates the mixed-mode I/II fracture behavior of O-notched diagonally loaded square plate (DLSP) samples containing an edge crack within the O-notch. This investigation aims to explore the combined effects of loading rate and mode mixity on the fracture properties of steel 304L, utilizing DLSP samples. The DLSP samples, made from strain-hardening steel 304L, were tested at three different loading rates: 1, 50, and 400 mm/min, covering five mode mixities from pure mode I to pure mode II. Additionally, tensile tests were performed on dumbbell-shaped specimens at the same loading rates to examine their influence on the material's mechanical properties. The findings revealed that stress and strain diagrams derived from the dumbbell-shaped samples were largely independent of the tested loading rates (i.e., 1-400 mm/min). Furthermore, experimental results from DLSP samples showed no significant impact of the loading rates on the maximum load values, but did indicate an increase in the ultimate displacement. In contrast to the loading rate, mode mixity exhibited a notable effect on the fracture behavior of DLSP samples. Ultimately, it was observed that the loading rate had an insignificant effect on the fracture path or trajectory of the tested DLSP samples.

A compact system for accurate measurement of true stress-strain curves in transparent materials subject to extensive deformation

Accurate quantification of the true stress-strain curve over an extensive strain range is pivotal for elucidating material mechanical properties and simulating non-linear plastic deformation. A novel experimental approach was developed to directly measure true stress-strain behavior in transparent materials. Our setup featured a single 3CCD camera and mirrors, capturing images of both specimen surfaces with bicolored fluorescent speckle patterns. Initially, we determined and corrected the specimen’s refractive index using a point-by-point least squares method. Subsequently, we used multispectral dual 3D digital image correlation (DIC) to reconstruct surface profiles and correct refractive distortions. This allowed precise computation of the deformed cross-sectional area over an expansive strain range. True stress was calculated from the measured engineering stress and computed deformed area. Validity was confirmed by deforming a fluorescent elastomer, and results aligned with the theoretical predictions. This compact experimental setup effectively evaluates true stress-strain relationships in transparent materials under extensive deformation.

Research on the Fracture Propagation Law of Separate Layered Fracturing in Unconventional Sandstone Reservoirs

The unconsolidated sandstone is a type of rock that has poor cementation, a low strength, a high porosity, and permeability. It is highly compressible under high stress and exhibits non-linear plastic deformation during hydraulic fracturing construction in its reservoir. In this study, the mechanical properties of unconsolidated sandstone with a different permeability were studied, and a three-dimensional hydraulic fracture propagation numerical model was established based on the modified traditional Cambridge model. This model was used to simulate the fracture propagation law of unconsolidated sandstone in separate layer fracturing under different construction conditions. During hydraulic fracturing construction, the fracturing fluid slowly invades the reservoir when the displacement of the fracturing fluid is small. The unconsolidated sandstone undergoes compaction and hardening, followed by shear expansion, and then complete destruction. A larger displacement will cause the reservoir rock to directly enter the state of destruction from compaction and hardening. This study found that several critical parameters are obtained for fracturing construction. When the displacement is greater than 5 m3/min, the fracturing fluid exceeds 100 mPa·s, or when the filtration coefficient exceeds 1.2 × 10−3 m/s, the second and third layers will be penetrated. This study provides valuable insights into the mechanical properties of unconsolidated sandstone and reveals the critical parameters for the successful hydraulic fracturing construction in this type of reservoir.

Ultrasonic Nonlinearity Experiment due to Plastic Deformation of Aluminum Plate Due to Bending Damage.

The nonlinear ultrasonic evaluation technique is useful for assessing micro-defects and microstructure changes caused by fatigue or bending damage. In particular, the guided wave is advantageous for long-distance testing such as piping and plate. Despite these advantages, the study of nonlinear guided wave propagation has received relatively less attention compared to bulk wave techniques. Furthermore, there is a lack of research on the correlation between nonlinear parameters and material properties. In this study, the relationship between nonlinear parameters and plastic deformation resulting from bending damage was experimentally investigated using Lamb waves. The findings indicated an increase in the nonlinear parameter for the specimen, which was loaded within the elastic limit. Inversely, regions of maximum deflection in specimens with plastic deformation exhibited a decrease in the nonlinear parameter. This research is expected to be helpful for maintenance technology in the nuclear power plant and aerospace fields that require high reliability and accuracy.

Physico-mechanical properties and brittle to plastic transition of a thermally cracked marble under uniaxial tension

Thermal stress induces severe changes in rock microstructures, resulting in the variations of physical and mechanical properties. To study thermal effects on rock physical properties and tensile behaviors, monotonic and cyclic tension tests were conducted on marble samples heated at different temperatures. The results show that marble samples are weakened by thermal damage, showing a decrease in tensile strength and P-wave velocity, and an increase in porosity. The changing trends of Young's modulus and failure strain with temperature appear to be scattering and complicated probably depending on the deformation types (i.e., nonlinear elastic deformation and plastic deformation). Nonlinearity is a fundamental feature of tensile stress versus strain curves, which is enhanced when the sample is heated at higher temperature. Even under low tensile stress levels, permanent damages are always observed, highlighting a hysteresis in the stress-strain curves obtained from cyclic tension tests. A transition from the nonlinear elastic deformation to the plastic deformation occurs at approximately 300 - 400°C. A crack density based constitutive model is introduced for the nonlinear elastic deformation (25 - 300°C). A modified Voce exponential function is recommended to capture the tensile stress and strain relationships for the plastic deformation (400 - 700°C).

Nonlinear FE-analysis and testing of light-frame timber shear walls subjected to cyclic loading

Light-frame timber shear walls have been used as load-bearing elements in buildings for several decades. To predict the performance of such structural elements under loading, numerous analytical and numerical models have been developed. However, little focus has been on the prediction of the plastic damage behaviour and unloading of the walls. In this paper, a parametric Finite Element (FE) model is further developed by introducing elasto-plastic connectors to simulate the mechanical behaviour of the sheathing-to-framing connections. To verify the accuracy of the elasto-plastic model, full-size walls were tested and compared with results from simulations. The numerical results, from a few loading cycles, indicate that the model achieves reasonable accuracy in predicting both the nonlinear elastic and plastic deformations. Both experimental and simulation results demonstrate the importance of opening locations relating to the external racking force. The results also indicate that for a double-layer wall, its racking strength can be achieved by summation of the separate contribution from each layer. Furthermore, the internal layer was observed to contribute significantly less than the external layer since its nail pattern was based on the sheathing pattern of the external layer.

A nonlinear elasto-plastic bond model for the discrete element modeling of woody biomass particles

This work presents an experiment-informed, semi-empirical, elasto-plastic bond model for the discrete element modeling of woody biomass particles. The model renders nonlinear plastic deformation of materials when subjected to compression/tension, bending, and twisting, essential for accurately simulating the behavior of biomass in comminution. The model is implemented in an open-source DEM package LIGGGHTS and is assessed in a number of verification tests. The model is applied to simulate the fracturing test of notched loblolly pine blocks. Reduced bond strength is prescribed to the weak planes along the growth rings. It is found that the square-root formulation for describing the elasto-plastic normal bond contact delivers the best agreement with the experimental data over its linear and quadratic counterparts. Furthermore, the model predicts a strong anisotropic behavior of wood blocks with regard to the grain orientations, indicating that the cutting angle should be an important attribute for the optimization of biomass comminution.

ТЕОРИЯ НЕЛИНЕЙНОЙ УПРУГОПЛАСТИЧЕСКИВЯЗКОЖЕСТКОЙ ДЕФОРМАЦИИ ПРЕДЕЛЬНО-НАПРЯЖЕННЫХ ГРУНТОВ В ОСНОВАНИЯХ НАГРУЖАЕМЫХ ОДИНОЧНЫХ СВАЙ: МАТЕМАТИЧЕСКАЯ МОДЕЛЬ

Research was carried out in accordance with the well-known necessity to elaborate a unified theory of nonlinear elastic-plastic-viscous rigid deformation of extremely strained granular soils in the bases of loaded single piles. Basic provisions of the model of the theory of nonlinear deformation of extremely strained soils are determined. Distinctive features of granular media in the role of models of mechanical behavior of dusty-clay and sandy soils under load are studied. Differential analysis of deformation of an experimentally studied base of a stamp is carried out; as a result, techniques for the following procedures has been developed: construction of separate design graphs of elastic, plastic, viscous and rigid soil deformations; theoretical determination of nonlinear general, elastic, plastic, viscous and rigid soil deformations; estimated determination of reference stepwise coefficients of proportionality of modules of nonlinear general, elastic, plastic, viscous and rigid soil deformations; approaches to simulation of granular media of dusty-clay and sandy soils. Studied forms of soil cores compacted at the base of a die and the lower ends of the single piles under research are described. A theory of geometric parameters and their correlations of strained deformed states of the soil is elaborated. Generalized conclusions on the essence of the content of the developed theory’s provisions are made.

A NOVEL EVALUATION APPROACH FOR SHALE BRITTLENESS INDEX

Brittleness index (BI) is a key parameter used for reservoir fracability evaluation and "sweet spot" search in shale gas exploration. The existing assessment methods cannot guide the fracturing design and field treatment due to their insufficient theoretical foundation and neglect on the influences of engineering factors. This study aims to solve this problem by using the thermodynamics criterion in nonlinear fracture mechanics. First, the quantitative relationship between energy loss and rock brittleness was investigated during fracture propagation. The nonlinear plastic deformation at the crack tip was then simplified into an ideal line elastic condition by using the equivalence principle. In addition, the numerical equation for surface pressure was fitted by the monadic regressive method. A case study was conducted to compare the obtained BI using common methods and the proposed one. Results demonstrate that energy dissipation theory is recommended to describe the essence of nonlinear rock deformation. Moreover, a higher BI indicates more occurrences of microseismic events. The monitoring data fitted with the conclusion well, which verify the applicability of the proposed evaluation method. Furthermore, the average BIs of the two wells used in this study are 48% and 62%, which shows obvious positive correlation with production. The proposed model can be regarded as a good reference for BI evaluation in shale reservoirs. Keywords: Brittleness index, Shale gas, Hydraulic fracturing, fracability

Mechanical behavior of fine-grained sandstone in triaxial compression and elastoplastic modeling by return mapping algorithms

The study is devoted to the strength and deformation behavior of fine-grained sandstone. A series of triaxial compression tests were conducted on rock samples under various confining pressures (3, 5, 10, 15, and 20 MPa) in the laboratory. The experimental results showed that the nonlinear behavior and plastic deformation of the sandstone are prominent during loading process. The peak strength of the sandstone can be enhanced with the increase of the confining pressure. The initial yield stresses σy are approximately 87.2%, 80.2%, 62.1%, 75.2%, and 83.8% of the peak strengths σ p , respectively. The shear failure is predominated failure mode under different confining pressures. Based on experimental results, an elastoplastic model is proposed using a linear yield function in p-q plane, as well as a non-associated plastic potential function. Furthermore, the numerical formulations of a return mapping algorithm for constitutive model implementation are introduced in this work. The numerical results agree well with the experimental data, which show that this model is able to describe the elastoplastic behavior of the sandstone under triaxial compression.

Effects of creep-plastic behavior on stress development in TBCs during cooling

Abstract The stress development, as the main cause of TBCs failure, can be significantly influenced by the non-linear behaviors of TBCs materials (e.g. plastic and creep deformations). Description of the non-linear behaviors of TBCs materials is crucial to accurate stress evaluation. However, conventional constitutive models couldn't distinguish the role of the nonlinear plastic and creep deformations in the stress evaluation, which may lead to obvious difference. This work employs the creep-plastic constitutive model to study the effects of creep-plastic behavior of BC and TGO on the TC/TGO/BC interface stress development. This creep-plastic model reveals that the stress can be identified in three sections when BC creep properties varies in wide margins: In the first section with a small BC creep rate, plastic deformation mainly influences the interface stresses; in the second section with a medium creep rate, both creep and plastic deformations affect the stress development; in the third section with a larger creep rate, creep becomes the main factor dominating the relaxing process. It is also found that if the creep in TGO is considered, the stresses will be overall relaxed no matter if BC is plastic, creep or creep-plastic. Based on this three-section phenomenon, the influence of TGO thickness, interface roughness and cooling rate on the stress development is investigated.

Testing and modeling of the mechanical behavior of dolomite in the Wudongde hydropower plant

ABSTRACTIn order to understand the mechanical behaviours of the surrounding rocks in the underground caverns of the Wudongde hydropower plant, triaxial tests are performed on a type of dolomite. It is revealed that damage induced by crack development is the main factor controlling the nonlinear plastic deformation and failure behaviour of the dolomite in both pre- and post-peak regimes. Based on this understanding, a coupled elastoplastic damage model is developed for capturing the dolomite’s mechanical behaviours. In the model, the effects of plasticity and damage on rocks is described by introducing plastic hardening and damage softening commonly in the plastic yield surface. Which are both derived from a suitable Helmholtz free energy function. The model is used to simulate the triaxial tests. Comparisons between test results and the numerical modelling show that the developed model is capable of describing the macro mechanical behaviours of the Wudongde dolomite.

Development of simulation system for large H-beam hot rolling based on ABAQUS

H-beam is a kind of efficient economic cross-section steel with wide flange and thin web. Due to the superior cross-section properties and reasonable strength-to-weight ratio benefiting from its especial shape, H-beam has been widely used in the industry and building trade. However, since the hot rolling of large H-beam is a highly nonlinear plastic deformation process which happens under the high temperature and high pressure, the real-time detection of internal information for H-beam and deformable roller in the rolling process is difficult to be realized. The finite element simulation is an effective measure to demonstrate the internal information during the whole hot rolling process. However, the drastic plastic deformation involved in the transient rolling process may lead to meshing distortion in simulation which would result into inaccurate simulation results. In this paper, the finite element simulation system for large H-beam hot rolling is developed based on ABAQUS and thermal coupled elastic-plastic finite element method by customizing applications and embedding re-meshing algorithm and subroutines. Modeling of pre-processing and extracting simulation results of post-processing can be automatically achieved through the simulation system. The re-meshing algorithm and the information transfer method of the clearance between two passes are synthetically used to ensure the continuous simulation of multi-pass hot rolling process and improve the accuracy of simulation results. The validity of the simulation system developed in this paper is verified through measuring the temperature field in hot rolling process of HN900x300 using a thermal infrared imager. The results show that the simulation results of the system are coincident with the measured results with errors below 6 %.

Characterization of local strain/stress in copper through-silicon via structures using synchrotron x-ray microdiffraction, electron backscattered diffraction and nonlinear thermomechanical model

In this study, the thermomechanical characteristics of copper through-silicon via (Cu TSV) structures were studied using synchrotron x-ray microdiffraction, electron backscattered diffraction (EBSD), and nonlinear numerical modeling. The strain and stress distribution in the Si substrate was measured by synchrotron x-ray microdiffraction from the tops of the TSV structures. The strain distribution map in a Cu via was determined from EBSD data by the kernel average misorientation (KAM) method and microstructural characteristics of the Cu via were investigated. The results offered direct evaluation of the local strain and stress induced in the Cu via and its surrounding silicon substrate. A finite element model including nonlinear plastic deformation was built for predicting thermomechanical behaviors of Cu TSV structures. The results show that the stress distribution obtained by finite element modeling is in relatively good agreement with the measurements of synchrotron x-ray microdiffraction and EBSD.

806 クロスプライCFRP積層板のプライベース疲労寿命予測法の開発(OS8-(2),OS8 オーガナイズドセッション《複合材料の変形と破壊およびマルチスケール計算技術》)

A ply-by-ply basis fatigue life prediction method for multi-directional composite laminates that can be applied to fatigue loading at any stress ratio has been developed, taking into account the inelastic deformation and in-situ strength of plies embedded in the laminates. Fatigue failure in embedded plies is evaluated using a quasi-static failure criterion based on the residual principal strengths. The residual principal strengths of unidirectional plies are predicted using the anisomorphic constant fatigue life diagrams that are identified for loading in the principal directions, respectively. The fatigue failure criterion for plies takes into account not only the in-situ principal strengths of plies embedded in a general laminate, but also the progressive reduction in in-situ constraint effect due to the growth of fatigue damage. The actual stress components in the plies embedded in a laminate are evaluated using a laminate constitutive model based on the classical lamination theory, in which the nonlinear plastic deformation of inclined plies under in-plane off-axis loading is taken into account. It is demonstrated that the proposed ply-by-ply basis fatigue model can successfully be used for prediction of on-axis and off-axis fatigue lives of cross-ply CFRP laminates that are subjected to fatigue loading at different stress ratios, respectively.

Influence of Combined Loading on Microstructure and Properties of Aluminum Alloy 2024-T3

The article gives results of the experimental study of mechanical properties and structure of the fractured specimens of multiphase aluminum-base alloy 2024-T3, which were deformed under the dynamic tension conditions. The study shows that the impact in an elastic region leads to an insignificant non-stationary deformation (i.e., deformation in the impact application process) and an insignificant weakening of the material, whereas in the presence of the appreciable plastic deformation before the impact the non-stationary deformation increases more than by an order of magnitude, and a marked weakening takes place. The effects observed are related to the synergy of structure under non-stationary loading. It was concluded that self-organization of the crystalline structure defects in the form of hydrodynamic flow channels, leading to increase in ductility and weakening, may occur only under the nonlinear (plastic) deformation conditions. In the elastic region, the synergic structure formation is limited only to a change of phase composition of the alloy, which may lead to premature fracture of the material under subsequent static deformation. This makes it impossible to predict durability of the material at a probability of uncontrollable load surges. Statistical examination of structure of the fractured specimens revealed the presence of the relaxation structure in the form of recrystallized grains of different sizes, characterized by the presence of scale invariance (scaling). As shown by the grain size analysis, the process of coarsening of the recrystallized grains under dynamic loading and fracture is controlled by some cooperative process related to the atomic and probably electronic structure of the deformed material.

The use of stress sweep tests for asphalt mixtures nonlinear viscoelastic and fatigue damage responses identification

Asphaltic materials are known to present a behavior that can be approximated by the theory of viscoelasticity. For these materials it is essential to characterize fatigue damage. An important aspect therein is the separation between nonlinear viscoelastic and fatigue damage responses. This is a complex issue, since both nonlinearity and damage have a similar effect on the overall material mechanical behavior, i.e. decrease in the stiffness and increase in the phase angle. This paper presents an experimental and a mathematical procedure to separate the nonlinear viscoelastic from the fatigue damage response for asphaltic materials. Stress sweep tests were used to characterize a hot mixture asphalt at nine conditions (three temperatures and three frequencies). Once all strain values were obtained in a stress controlled sweep test, a statistical analysis was used to find the maximum stress that can be applied to the material without invoking the damage response. The results showed that the transition stress value is directly associated with material properties, the stiffness being an important factor in this result. Consequently, stress, temperature and frequency determine together the mechanical response of the material (linear or nonlinear viscoelastic, fatigue damage and/or plastic deformation). Results from this study can be associated with other fatigue damage approaches in order to better select the stress or strain amplitude that should be used in fatigue tests, and to eliminate the amount of energy that is dissipated in the nonlinear viscoelastic region.

Mechanical and magnetic properties of ZnO/Fe2O3 ceramic varistors

Mechanical and magnetic properties of the ZnO/Fe2O3 ceramic varistors have been examined by using mechanical analyzer, digital microhardness tester and vibrating sample magnetometer. The initial stress–strain behavior is found to be linear (elastic) then becomes nonlinear (plastic deformation) without reaching the failure limit up to the maximum available stress (0.07MPa). The compressive elastic modulus varies between 0.2 and 0.8MPa with Fe addition up to 0.50. Furthermore, an approximately monotonically linear decrease in VHN with increasing Fe content up to 50% has been observed for all applied loads, which closely resembles the behavior of the true hardness and the surface energy. The magnetic measurements revealed an antiferromagnetic to paramagnetic to transition for all Fe doped samples. The Fe free sample showed paramagnetic behavior down to 2K. The Neel temperature moderately increased from 18K at 0.05% Fe to 25K at 0.5% Fe. The magnetization (M) versus applied magnetic field (H) did not reach saturation for all samples up to 9Tesla. The saturated magnetization (per Fe contents) is low and found to decreases linearly at a rate of (−35emu/g-Fe) in a clear manifestation of the strengthening of the antiferromagnetic exchange interaction with increasing Fe contents.