Triaxial Compression Stress State Research Articles

Plastic deformation mechanisms of FeSiCrNi high silicon steel based on local canning compression

High silicon steel has excellent soft magnetic properties, but a poor plasticity limits its practical application seriously. In this research, a novel FeSiCrNi alloy short for Fe-6.5Si–2Cr–12Ni (wt%) was designed and deformed via the local canning compression process at room temperature. It was shown that the FeSiCrNi alloy presents a relatively high plasticity in a triaxial compressive stress state. Geometrically necessary dislocations ensure the compatibility of plastic deformation for FeSiCrNi alloy. There are a small number of η and γ textures inside the FeSiCrNi sample. The intensity of η texture nearly keeps steady, while the intensity of γ texture increases slightly with the level of plastic deformation increasing. Additionally, the intensity of {112}<111> copper texture increases with the increase of plastic deformation. Lath structures dominate the inhomogeneous plastic deformation of FeSiCrNi alloy and then integrate with the phase α-Fe. The main deformation mechanism of FeSiCrNi alloy is dislocation slip rather than twinning which has not been observed yet. The order degree of FeSiCrNi alloy continuously decreases, and deformation bands, dislocation walls and dislocation cells are successively formed, as the compression proceeds. It is feasible to produce FeSiCrNi components in cold forming process.

Time-Temperature-Stress Equivalent Characteristics and Nonlinear Viscoelastic Model of Asphalt Mixture under Triaxial Compressive Stress State

Time-Temperature-Stress Equivalent Characteristics and Nonlinear Viscoelastic Model of Asphalt Mixture under Triaxial Compressive Stress State

A Multiscale Method to Develop Three-Dimensional Anisotropic Constitutive Model for Soils

A multiscale method is presented to develop a constitutive model for anisotropic soils in a three-dimensional (3D) stress state. A fabric tensor and its evolution, which quantify the particle arrangement at the microscale, are adopted to describe the effects of the inherent and induced anisotropy on the mechanical behaviors at the macroscale. Using two steps of stress mapping, the deformation and failure of anisotropic soil under the 3D stress state are equivalent to those of isotropic soil under the triaxial compression stress state. A series of discrete element method (DEM) simulations are conducted to preliminarily verify this equivalence. Based on the above method, the obtained anisotropic yield surface is continuous and smooth. Then, a fabric evolution law is established according to the DEM simulation results. Compared with the rotational hardening law, the fabric evolution law can also make the yield surface rotate during the loading process, and it can grasp the microscopic mechanism of soil deformation. As an example, an anisotropic modified Cam-clay model is developed, and its performance validates the ability of the proposed method to account for the effect of soil anisotropy.

Influence of intermediate principal stress ratio on strength and deformation characteristics of frozen sandy soil under different moisture contents

Frozen ground often contain non-uniform moisture content and are under true triaxial stress state and their practical engineering application are still explored. The present study is carried out to investigate the strength and deformation characteristics of frozen soil with different moisture contents under true triaxial stress state conditions. A series of true triaxial tests were conducted on frozen soil specimens having constant minimum principal stress (σ3) and constant intermediate principal stress ratio (b). The experimental test results showed that the stress-strain curves represent the strain-hardening characteristics under different test conditions. The intermediate principal stress ratio (b) has a dual effect of strengthening and weakening on the strength of frozen sandy soil. When 0 ≤ b ≤ 0.5, the strengthening effect was found to be dominant in the frozen soil specimen, whereas, the weakening effect was dominant when 0.5 < b ≤ 1. The strength of frozen soil under true triaxial stress state is 8.18% to 36.33% higher under different water content conditions, compared to that under generalized triaxial compression stress state. The difference in deformation between the direction of the intermediate principal stress and the minimum principal stress increased with the increment in the intermediate principal stress ratio value. The volumetric strain in the soil sample initially exhibited the characteristics of shear contraction and then shear dilation.

Hydromechanical behaviors of andesite under different stress states during fluid injection

Water reinjection into the formation is an indispensable operation in many energy engineering practices. This operation involves a complex hydromechanical (HM) coupling process and sometimes even causes unpredictable disasters, such as induced seismicity. It is acknowledged that the relative magnitude and direction of the principal stresses significantly influence the HM behaviors of rocks during injection. However, due to the limitations of current testing techniques, it is still difficult to comprehensively conduct laboratory injection tests under various stress conditions, such as in triaxial extension stress states. To this end, a numerical study of HM changes in rocks during injection under different stress states is conducted. In this model, the saturated rock is first loaded to the target stress state under drainage conditions, and then the stress state is maintained and water is injected from the top to simulate the formation injection operation. Particular attention is given to the difference in HM changes under triaxial compression and extension stresses. This includes the differences in the pore pressure propagation, mean effective stress, volumetric strain, and stress-induced permeability. The numerical results demonstrate that the differential stress will significantly affect the HM behaviors of rocks, but the degree of influence is different under the two triaxial stress states. The HM changes caused by the triaxial compression stress states are generally greater than those of extension, but the differences decrease with increasing differential stress, indicating that the increase in the differential stress will weaken the impact of the stress state on the HM response. In addition, the shear failure potential of fracture planes with various inclination angles is analyzed and summarized under different stress states. It is recommended that engineers could design suitable injection schemes according to different tectonic stress fields versus fault occurrence to reduce the risk of injection-induced seismicity. • A numerical model of the hydromechanical coupling process during injection is established and verified based on laboratory testing data. • The effects of three stress states on the hydromechanical behavior and the shear failure potential of rocks are studied, the differences in hydromechanical changes under triaxial compression and extension stress states are studied.

Scratch behavior of polycarbonate by Rockwell C diamond indenter under progressive loading

Rockwell C diamond indenter with a spherical tip of radius of 108 μm was used to slide on bulk polycarbonate under linearly increasing normal load from 5 mN to 20 N in order to investigate deformation and damage of ductile polymers during scratching. The peak value of the ratio of residual depth over penetration depth corresponds to a critical normal load, which can be used as the piecewise point for the subsection functions describing variation of tangential load, penetration depth and residual depth with normal load. The true adhesion interfacial friction coefficient was found to be 0.3 for contact between PC and diamond by three-dimensional model. Residual groove widths were found to be proportional to the square root of normal load, and provided useful information to characterize the radius of spherical tip. Values of fracture toughness of PC obtained by scratch-based methodologies under sufficiently large normal loads associated with brittle fracture and crack plane, are in excellent agreement with literature values. The material is under triaxial compressive stress state, making the flow and shear stresses much larger than the ones for uniaxial tensile test.

A constitutive model for granular materials subjected to a large stress range

Abstract A simple constitutive model is presented to represent the behavior of granular materials subjected to a large stress range by introducing a revised normal compression line with a limit void ratio (eL) in the double logarithmic scale and a state parameter (ξ) to quantify the state of granular materials. In the proposed model, a drop-shaped yield surface is employed and a unified hardening parameter (H) that is a function of the state parameter (ξ) is developed to govern the hardening process. The model is first established in the triaxial compression stress state and then is extended to the general stress state through the transformed stress (TS) method. Adopting a single set of material parameters, the proposed model is verified against the experimental results of various tests on Cambria sand at different confining pressures (0.25–68.9 MPa), including the data of isotropic compression test and drained/undrained triaxial compression/extension tests.

Experimental investigation of the effect of compliant pores on reservoir rocks under hydrostatic and triaxial compression stress states

The presence of compliant pores in rocks is important for understanding the stress–strain behaviors under different stress conditions. This paper describes findings on the effect of compliant pores on the mechanical behavior of a reservoir sandstone under hydrostatic and triaxial compression. Laboratory experiments were conducted at reservoir temperature on Weber Sandstone samples from the Rock Springs Uplift, Wyoming. Each experiment was conducted at three sequential stages: (stage 1) increase in the confining pressure while maintaining the pore pressure, (stage 2) increase in the pore pressure while maintaining the confining pressure, and (stage 3) application of the deviatoric load to failure. The nonlinear pore pressure – volumetric strain relationship governed by compliant pores under low confining pressure changes to a linear behavior governed by stiff pores under higher confining pressure. The estimated compressibilities of the matrix material in sandstone samples are close to the typical compressibility of quartz. Because of the change in pore structures during stage 1 and stage 2 loadings, the estimated bulk compressibilities of the sandstone sample under the lowest confining pressure decrease with increasing differential pressure. The increase in crack initiation stress is limited with increasing differential pressure because of similar total crack length governed by initial compliant porosity in sandstone samples.

Experimental Study of Failure Differences in Hard Rock Under True Triaxial Compression

In view of a previous study of the intermediate principal stress effect at a limited σ2 range, a series of true triaxial tests, covering a full range of intermediate principal stresses that vary from the generalized triaxial compression stress state (σ2 = σ3) to the generalized triaxial tensile stress state (σ1 = σ2), was carried out on sandstone and granite samples. The experimental results revealed that the deformation, failure strength and failure mode have a significant dependence on the stress state. As an effect of the intermediate principal stress on crack evolution, the deformation difference known as stress-induced deformation anisotropy occurred and should be considered when developing the mechanical model. Moreover, a post-peak deformation with a step-shaped stress drop is observed and illustrates that there will be a multi-stage bearing capacity after the rock failure. The peak strength is non-symmetrical with the increasing σ2 and is closely related to the Lode angle. Based on the final fracture surface and SEM analysis under true triaxial compression, three failure modes and failure zones, including tension failure, shear failure and mixed failure, are delineated and discussed. Combining the failure mode and the strength under true triaxial compression, it is found that the strength variation exhibited a close relationship to the failure mechanism.

Design of packing cup interference fit value of hypercompressors for low density polyethylene production

The hypercompressor is one of the core facilities in low density polyethylene production, with a discharge pressure of approximately 300 MPa. A packing cup is the basic unit of cylinder packing, assembled by the interference fit between an inner cup and an outer cup. Because the shrink-fitting prestresses the packing cup, serious design is needed to gain a favorable stress state, for example, a tri-axial compressive stress state. The traditional method of designing the interference fit value for packing cups depends on the shrink-fit theory for thickwalled cylinder subject to internal and external pressure. According to the traditional method, critical points are at the inner radii of the inner and external cup. In this study, the finite element method (FEM) has been implemented to determine a more accurate stress level of packing cups. Different critical points have been found at the edge of lapped sealing surfaces between two adjacent packing cups. The maximum Von Mises equivalent stress in a packing cup increases after a decline with the rise of the interference fit value. The maximum equivalent stress initially occurs at the bore of the inner cup, then at the edge of lapped mating surfaces, and finally at the bore of the outer cup, as the interference radius increases. The traditional method neglects the influence of axial preloading on the interference mating pressure. As a result, it predicts a lower equivalent stress at the bore of the external cup. A higher interference fit value accepted by the traditional method may not be feasible as it might already make packing cups yield at the edge of mating surfaces or the bore of the external cup. Along with fatigue analysis, the feasible range of interference fit value has been modified by utilizing FEM. The modified range tends to be narrower and safer than the one derived from the traditional method, after getting rid of shrink-fit values that could result in yielding in a real packing cup.

Analysis and design of cross wedge rolling hollow axle sleeve with mandrel

Axle sleeves are important parts of the drive axle for truck and construction machinery, and their large demand requires an efficient production process. Cross wedge rolling axle sleeves with mandrel can save material and enhance efficiency; however, axial movement and ovality are common problems if no stub bars are expected when hollow stepped axle sleeves with gradually reduced diameters in one direction are formed by cross wedge rolling. In this paper, the process of cross wedge rolling axle sleeves proximately without a stub bar was developed by using a combination of finite element simulation and experiments. On the basis of the simulation analysis, the process design of cross wedge rolling axle sleeves was improved to avoid axial movement and ovality. The field of strain and stress demonstrated that the deformation of cross wedge rolling axle sleeve with mandrel primarily took place in the triaxial compressive stress state, thereby significantly improving the microstructure. The hole expansion at the knifing position of the workpiece was analyzed and resolved by mandrel compensation. The simulation results were verified by experiments, and an economic and efficient formation method to produce an axle sleeve was achieved in this study.

A Comparison of Hot Deformation Behavior of High‐Cr White Cast Iron and High‐Cr White Cast Iron/Low Carbon Steel Laminate

In order to study the plastic deformation characteristics of the brittle high‐Cr white cast iron in upsetting process, and find out the mechanism for improving the formability of the cast iron within the laminated composite, the hot forging process of monolithic high‐Cr white cast iron and high‐Cr white cast iron/low carbon steel laminate is simulated by means of hot compression tests using Gleeble 3500 thermo mechanical simulator and professional plastic forming software DEFORM‐3D. The results reveal that during hot compression process, the monolithic cast iron suffered severe barreling and cracking, whereas the cast iron layer within the laminate underwent large plastic deformation with barreling‐free and crack‐free. Such a significant improvement can be attributed to the simultaneous deformation of the cast iron together with the low carbon steel claddings, which is beneficial to relieving the stress in the cast iron and changing its deformation mode. Under the triaxial compressive stress state, the brittle high‐Cr white cast iron within the laminate can flow like a ductile material at high temperatures and low strain rates.

Time-Dependent Unified Hardening Model: Three-Dimensional Elastoviscoplastic Constitutive Model for Clays

AbstractA new three-dimensional (3D) elastoviscoplastic (EVP) constitutive model for both normally consolidated and overconsolidated clays is presented. In developing the new model, first the time effects on clays were connected with the change of overconsolidation degree according to the concepts of aging time and the instant normal compression line. This made it convenient to combine a logarithmic creep function with the reloading function of the unified hardening (UH) model (a model for overconsolidated clays), and, thus, an isotropic EVP relationship was built. Second, a time variable derived from the isotropic EVP relationship was embedded into the current yield function of the UH model, and, thereby, a time-dependent current yield function is proposed. Based on the time-dependent current yield function and the flow rule, an EVP model for triaxial compression stress states was built. The EVP model for triaxial compression stress states then was extended to a 3D EVP model for general stress states thr...

The Explanation of Yield Surface Rotation of Sands by Principle of Thermodynamics with Internal Variables

&lt;p class="p18"&gt;Using constitutive modelling principle of thermodynamics with internal variables, the yield surfaces rotation of saturated sands subjected triaxial compression stress state are justified and explained. The explanation for the yield surfaces rotation of saturated sands prove the correctness and feasibility for the principle of thermodynamics with internal variables to construct elastoplastic constitutive relation of saturated soils.&lt;/p&gt;

Mechanical behavior and failure criterion of the gangue-based haydite concrete under triaxial loading

Triaxial loading tests were carried out on the gangue-based haydite concrete cube specimens (100 × 100 × 100 mm3) and plate specimens (100 × 100 × 50 mm3) to investigate the mechanical behavior of this kind of lightweight aggregate concrete (LWAC) under multi-axial stress state, and accordingly to develop the failure criterion for the finite element analysis of LWAC structures. Experimental results revealed that, under triaxial compression loading, most of the haydites within the specimen were crushed when the stress ratios σ 1/ σ 3 ≥ 0.3 and σ 2/ σ 3 ≥ 0.5. The gangue haydite concrete exhibited “plastic flow plateau” at this stage, which was conservatively regarded as the ultimate strength of the LWAC under triaxial compressive stress state. As a result, the tensile and compressive meridians on failure envelope surface are intersected with hydrostatic axial at two points, completely different from the characteristics of normal weight concrete for which the failure surface is unclosed and open-ended under compression. In terms of the test data, a four-parameter triaxial failure criterion for LWAC was developed. The strength envelope in the deviatoric plane adopted elliptic curve similar to that of Willam–Warnke model, and the tensile and compressive meridians were represented by quadratic functions with four parameters. Two alternative methods, i.e. the characteristic strength points method and the least square regression method, were used to determine the model parameters. After compared with the failure criterion recommended by fib Model Code 2010, methods proposed in this study are preferred especially when the plastic flow property is taken into account.

The Modified Cam-Clay Model and the Constitutive Relation Principle of Thermodynamics with Internal Variables

According the theory of thermodynamics with internal variables, the relation between yield function and dissipation function and the condition of associated flow rule in stress space are presented; the elastoplastic matrix of the incremental form of the material constitutive equation is given out, this matrix is determined by the free energy function and the yield function. The Gibbs free energy function of solid phase of saturated soils subjected triaxial compression stress state is presented, and using the constitutive theory of thermodynamics with internal variables, yield function and stress-strain relation of the modified Cam-Clay model is obtained by the free energy function and the dissipation function. These results prove the correctness and feasibility for this constitutive theory to construct elastoplastic constitutive relation of saturated soils.

The strength-dilatancy characteristics embraced in hypoplasticity

The strength-dilatancy characteristics of frictional materials embraced in the hypoplastic model proposed by Gudehus and Bauer are investigated and compared with the revised model suggested by Huang. In the latter the deviatoric stress in the model by Gudehus and Bauer is replaced by a transformed stress according to the stress transformation technique proposed by Matsuoka. The flow rule, the failure state surface equation and the strengthdilatancy relationship embraced in both models are derived analytically. The performance of the two hypoplastic models in reproducing the relationship between the peak strength and the corresponding dilation rate under triaxial compression, plane compression and plane shearing are then extensively investigated and compared with experimental results and with the predictions made by particular classical stress-dilatancy theories. Numerical investigations show that the performance in reproducing the strength-dilatancy relationship is quite satisfactory under triaxial compression stress state in both models and the predictions made by the transformed stress based model are closer to the results obtained from classical stress-dilatancy theories for plane compression and plane shearing problems.

Investigation into Lubliner yield criterion of concrete for 3D simulation

A class of widely used plastic-damage models for concrete employ the Lubliner yield criterion, whose properties in triaxial stress states have not received due attention. This paper intends to provide a thorough investigation into this strength theory for its application in 3D simulation of concrete structures. Its algebraic formulation and geometric representation are analyzed with a particular perspective on the similarity in form between the yield conditions in triaxial compression and other stress states, from which it is found that there is a strong dependence of triaxial tensile strength on the compressive cohesion and strength increase in triaxial compression fails to be described appropriately. Effective calibration methods are proposed for concrete under uniform and non-uniform confinement respectively to take into account both strength increase and strength ratio.

Test Study on Mechanical Characteristic of High Strength Composite Shaft Lining of Steel and Concrete

For the economic and reasonable application of high strength composite shaft lining of steel and concrete, the mechanical characteristic of this kind of structure were studied. First of all, according to the similarity theory, the shaft lining model is designed, then making the specimen and the loading test are put into effect. The results show that the combined action of inner and outer steel tube and middle concrete improves their respective performance. In shaft lining structure the stability of steel tube would be enhanced and the brittleness of high strength concrete would be improved also, so shaft lining structure shows fairly plastic feature when it is destroyed. Moreover, because of the restraint function of double-layer plate, the concrete in shaft lining structure completely is in triaxial compression stress state, the compressive strength can improve 1.53 ~ 1.90 times more than the concrete under uniaxial compression. The bearing capacity of shaft lining also increased greatly. Therefore, it is proposed that the improvement coefficient of the concrete’s compressive strength should be considered in the strength calculation of high composite shaft lining structure of steel and concrete.

An Improved Elasto-Plastic Model for Unsaturated Soils

The strength and deformation behaviors of unsaturated soil can be approximately described by elasto-plastic constitutive model that was proved by abundance academic and test researches. The Barcelona elastic-plastic model is an excellent model that can simulate the strength and deformation of unsaturated soil. But their calculated result of shear strength is low. So an improved Barcelona model is settled by using drop-shaped shear yield surface and hardening theory of dual stress. The results show that the improved model can more accurately predict the strength and deformation behaviors of unsaturated soil under suction-controlled triaxial compression stress states.