Influence of niobium and yttrium on plastic deformation energy and plasticity of Ti-based amorphous alloys

Many amorphous alloys have been developed to date,but the low plasticity has limited their application.To achieve an amorphous alloy with high plasticity,a series of(Ti_(40)Zr_(25)Cu_(9)Ni_(8) Be_(18))_(100-x)TM_(x)(x=0,1,2,3,4 at.%,TM=Nb,Y)alloys were designed to study the influence of Nb and Y addition on the plasticity.The amorphous samples were prepared using the vacuum melting and copper mold casting process.The microstructures,glass forming ability and mechanical properties of the alloys were investigated by X-ray diffractometry(XRD),scanning electron microscopy(SEM),high-resolution transmission electron microscopy(HRTEM),depth-sensitive nanoindentation,and uniaxial compressive test.The plasticity of different bulk amorphous alloys was investigated by measuring the plastic deformation energy(PDE)during loading.The relationship between the PDE value and plasticity in bulk amorphous alloys was explored.Results show that Nb addition decreases the PDE value and promotes the generation of multiple shear bands,which significantly increases the fracture strength and plasticity,while the addition of Y element reduces the fracture strength and plastic strain of the alloy.

Bauschinger and size effects in thin-film plasticity due to defect-energy of geometrical necessary dislocations

The Bauschinger and size effects in the thinfilm plasticity theory arising from the defect-energy of geometrically necessary dislocations （GNDs） are analytically investigated in this paper. Firstly, this defect-energy is deduced based on the elastic interactions of coupling dislocations （or pile-ups） moving on the closed neighboring slip plane. This energy is a quadratic function of the GNDs density, and includes an elastic interaction coefficient and an energetic length scale L. By incorporating it into the work- conjugate strain gradient plasticity theory of Gurtin, an energetic stress associated with this defect energy is obtained, which just plays the role of back stress in the kinematic hardening model. Then this back-stress hardening model is used to investigate the Bauschinger and size effects in the tension problem of single crystal Al films with passivation layers. The tension stress in the film shows a reverse dependence on the film thickness h. By comparing it with discrete-dislocation simulation results, the length scale L is determined, which is just several slip plane spacing, and accords well with our physical interpretation for the defect- energy. The Bauschinger effect after unloading is analyzed by combining this back-stress hardening model with a friction model. The effects of film thickness and pre-strain on the reversed plastic strain after unloading are quantified and qualitatively compared with experiment results.

Energy dissipation and contour integral characterizing fracture behavior of incremental plasticity

J ep -integral is derived for characterizing the frac- ture behavior of elastic-plastic materials. The J ep -integral differs from Rice’s J-integral in that the free energy density rather than the stress working density is employed to define energy-momentum tensor. The J ep -integral is proved to be path-dependent regardless of incremental plasticity and deformation plasticity. The J epintegral possesses clearly clear physical meaning： （1） the value J ep tip evaluated on the infinitely small contour surrounding the crack tip represents the crack tip energy dissipation; （2） when the global steadystate crack growth condition is approached, the value of J ep farss calculated along the boundary contour equals to the sum of crack tip dissipation and bulk dissipation of plastic zone. The theoretical results are verified by simulating mode I crack problems.

Stability and reinforcement analysis of rock slope based on elasto-plastic finite element method

The rigid body limit equilibrium method(RBLEM) and finite element method(FEM) are two widely used approaches for rock slope's stability analysis currently. RBLEM introduced plethoric assumptions; while traditional FEM relied on artificial factors when determining factor of safety(FOS) and sliding surfaces. Based on the definition of structure instability that an elasto-plastic structure is not stable if it is unable to satisfy simultaneously equilibrium condition, kinematical admissibility and constitutive equations under given external loads, deformation reinforcement theory(DRT) is developed. With this theory, plastic complementary energy(PCE) can be used to evaluate the overall stability of rock slope, and the unbalanced force beyond the yield surface could be the identification of local failure. Compared with traditional slope stability analysis approaches, the PCE norm curve to strength reduced factor is introduced and the unbalanced force is applied to the determination of key sliding surfaces and required reinforcement. Typical and important issues in rock slope stability are tested in TFINE(a three-dimensional nonlinear finite element program), which is further applied to several representatives of high rock slope's stability evaluation and reinforcement engineering practice in southwest of China.

Measurement of the Energy Absorbed during Nanoscale Deformation of Human Peritubular and Intertubular Dentin

Mineralized tissues are usually constructed of nanosized materials with ordered hierarchical structures. The main reason for their high load-bearing ability is the multi-scale hierarchy. It is important to have a method for measuring the energy absorbed during the nanoscale deformation of mineralized tissues. The objective of this study was to use a combination of nanoindentation and elastic-plastic mechanics techniques to measure the damage resistance of peritubular and intertubular dentin, based on the energy consumed in the plastic deformation regime and the volume created by the indents. The control materials were soda-lime glass, gold, and poly-methyl methacrylate (PMMA). Plastic deformation energy was calculated from the plastic part of load-displacement curves. The mean values of peritubular dentin and intertubular dentin were 3.8 × 109, and 5.2 × 109 J/m3, respectively, compared to glass, PMMA, and gold which were 3.3 × 107, 1.3 × 109, and 3.1 × 109 J/m3, respectively. This method can be applied to study the resistance of mineralized tissues or organic/inorganic hybrid materials to deformation at the nanoscale.

Elastoplastic damage model for concrete based on consistent free energy potential

The aim of this study is to formulate an appropriate free energy potential for inelastic behavior of concrete and construct an elastoplastic damage model on a more rational basis. The concept of effective plastic energy storage rates is proposed, which are conjugate forces of hardening variables in an undamaged configuration. Then an analogy between the evolution of harden- ing variables and that of a plastic strain is used to postulate the formulation of plastic free energy. This formulation reflects the specific characteristics of a certain plasticity model, so it can serve well as a thermodynamic link between plasticity and dam- age. By combination of the general formulation of free energy with the double hardening plasticity theory and two-parameter damage expression, a thermodynamically well-founded elastoplastic damage model for concrete is constructed. The operator split algorithm is emploved, and the numerical simulations a^ree well with a series of material tests.

Plastic Strain Energy Model for Rock Salt Under Fatigue Loading

The fatigue test for rock salt is conducted to investigate the effects of stress ampli- tude, loading frequency and loading rate on the plastic strain energy, from which the evaluation rule of the plastic strain energy is analyzed, which is divided into three stages： cyclic hardening, saturation and cyclic softening. The total accumulated plastic strain energy only depends on the mechanical behavior of rock salt, but is immune to the loading conditions. A novel model for fatigue life prediction is proposed based on the invariance of the total plastic dissipation energy and the stability of the plastic energy per cycle.

Modeling of state parameter and hardening function for granular materials

A modified plastic strain energy as hardening state parameter for dense sand was proposed, based on the results front a series of drained plane strain tests on saturated dense Japanese Toyoura sand with precise stress and strain measurements along many stress paths. In addition, a unique hardening function between the plastic strain energy and the instantaneous stress path was also presented, which was independent of stress history. The proposed state parameter and hardening function was directly verified by the simple numerical integration method. It is shown that the proposed hardening function is independent of stress history and stress path and is appropriate to be used as the hardening rule in constitutive modeling for dense sand, and it is also capable of simulating the effects on the de-formation characteristics of stress history and stress path for dense sand.

The hot compressive deformation behavior of cast Mg-Gd-Y-Zn-Zr alloys with and without LPSO phase in their initial microstructures

Samples of Mg-8.2Gd-3.8Y-1.1Zn-0.4Zr alloy with and without an intragranular lamellae-shaped long period stacking ordered(LPSO)phase were prepared through heat treatment and a series of hot compression tests on these materials were conducted to examine and evaluate the influence of LPSO on the hot compressive deformation behavior and deformation mechanisms at a given alloy composition.The values of activation energy for plastic flow(Qc)of the solution treated(without LPSO phase)and annealed alloys(with intragranular LPSO phase)were larger than that for pure Mg,indicating that the presence of a high amount of rare earth(RE)elements and LPSO in the Mg matrix significantly increases Qc.The Qcvalue of the annealed alloy was larger than that of the solution treated alloy at all the strain levels(223.3 vs.195.5 k J/mol in average)and the largest difference in Qcbetween the two alloys was recorded at the smallest strain of 0.1 where precipitation of LPSO during deformation was limited in the solution treated alloy.These observations imply that the formation of LPSO phase out of the RE-rich solid solution matrix during deformation increases Qc,but the increment is not so large.Analysis of the hot compressive data of the alloys with LPSO phase and the alloys with RE-rich solid solution matrix in literatures indicates the similarity of the effect of the LPSO and RE-rich solid solution matrix phases on Qcand high-temperature strength.

Stability and reinforcement analyses of high arch dams by considering deformation effects

The strict definition and logical description of the concept of structure stability and failure are presented. The criterion of structure stability is developed based on plastic complementary energy and its variation. It is presented that the principle of minimum plastic complementary energy is the combination of structure equilibrium, coordination condition of deformation and constitutive relationship. Based on the above arguments, the deformation reinforcement theory is developed. The structure global stability can be described by the relationship between the global degree of safety of structure and the plastic complementary energy. Correspondingly, the new idea is used in the evaluations of global stability, anchorage force of dam-toe, fracture of dam-heel and treatment of faults of high arch dams in China. The results show that the deformation reinforcement theory provides a uniform and practical theoretical framework and a valuable solution for the analysis of global stability, dam-heel cracking, dam-toe anchorage and reinforcement of faults of high arch dams and their foundations.

A DAMAGE FUNCTION USED FOR PREDICTION OF LOW CYCLIC FATIGUE LIFE

In this paper, the cyclic plastic strain energy is acted as damage variable and its mathematical model of transient response is established. The nonlinear fatigue damage function is given by means of the damage mechanical method. The formula used for prediction of low cyclic fatigue life is obtained from this damage function which takes into account the cyclic relativity of cyclic plastic strain energy. The low cyclic fatigue life predicted by this formula is in correspondence with the experimental result.

Deformation behavior of Fe-Mn-C TWIP steel within the temperature range of hot rolling

The hot-deformation behavior of Fe-Mn-C twinning induced plasticity （TWIP） steel was investigated by conducting hot compression tests within a recommended hot rolling temperature range at various strain rates. Flow resistance curves during hot-deformation were obtained, and strain rate sensitivities and activation energies for plastic deformation were calculated using the power law. It is found that the addition of Al and Si clearly increases the peak stresses for the present alloys, especially at 950℃. But Mn has a minor effect on the stress-strain curves and activation energy when its content varies from 15 mass% to 22 mass% for the present alloys.

Describing failure in geomaterials using second-order work approach

Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work,involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.

Energy Absorption and Deformation Mechanism of Lotus-type Porous Coppers in Perpendicular Direction

As metallic foams used for energy absorption in the automotive and aerospace industries, recently invented lotus-type porous metals are viewed as potential energy absorbers. Yet, solid conclusion on their eligibility as energy absorbers is still in question, particularly when compression is in the direction perpendicular to the axial orientation of cylindrical pores. In this work, the energy absorption of lotus-type porous coppers in the perpendicular direction is investigated at strain rates from 0.001 s^（-1） to^2400 s^（-1）. The energy absorption capacity and the energy absorption efficiency are calculated to be4–16 k J/kg and 0.32–0.7, respectively, slightly inferior to metal foams and the same porous solid compressed in the parallel direction due to the shortened extent of the plateau stress region. The deformation mechanism is examined experimentally in conjunction with finite element modeling. Both suggest that gradual squeeze and collapse of pores are the mechanisms accommodating the energy absorption. The deformation is generally evenly distributed over pore ligaments and independent of strain rate.

A Fully Coupled Thermomechanical Model of Friction Stir Welding(FSW) and Numerical Studies on Process Parameters of Lightweight Aluminum Alloy Joints

This paper presents a new thermomechanical model of friction stir welding which is capable of simulating the three major steps of friction stir welding （FSW） process, i.e., plunge, dwell, and travel stages. A rate-dependent Johnson- Cook constitutive model is chosen to capture elasto-plastic work deformations during FSW. Two different weld schedules （i.e., plunge rate, rotational speed, and weld speed） are validated by comparing simulated temperature profiles with experimental results. Based on this model, the influences of various welding parameters on temperatures and energy generation during the welding process are investigated. Numerical results show that maximum temperature in FSW process increases with the decrease in plunge rate, and the frictional energy increases almost linearly with respect to time for different rotational speeds. Furthermore, low rotational speeds cause inadequate temperature distribution due to low frictional and plastic dissipation energy which eventually results in weld defects. When both the weld speed and rotational speed are increased, the contribution of plastic dissipation energy increases significantly and improved weld quality can be expected.

Fracture analysis of rock mass based on 3-D nonlinear Finite Element Method

Traditional fracture analysis is based on fracture mechanics and damage mechanics. They focus on the propagation of the fracture. However, their propagation criterions are not easily applied in practice and the current analysis is limited in planar problem. This paper presents a new theory that the occurrence of the unbalanced force (derived from the Deformation Reinforcement Theory) could be the criterion of the initiation of the fracture, and the distribution area and propagation of the unbalanced force could be the indication of the fracture propagation direction. By aggregate analysis with Stress Intensity Factor (SIF) criterion, the unbalanced force actually is the opposite external load that is the SIF difference incurred between the external loads and permitted by the structure. Numerical simulation and physical experiments on pre-fracture cuboid rock specimens proved that the occurrence of the unbalanced force could be the initiation of the fracture. Mesh size dependence was also considered by analysis of different mesh size finite element gravity dam models. Furthermore, the theory was applied to the feasibility analysis of the Baihetan arch dam together with physical experiments in order to evaluate the fracture propagation of dam heel. The results show that it is an effective way to use unbalanced force to analyze the fracture initiation and propagation when performing 3-dimensional nonlinear FEM calculation.

Nanoindentation analysis of TiN,TiAlN,and TiAlSiN coatings prepared by cathode ion plating

The TiN, TiA1N and TiA1SiN coatings were deposited on H13 hot-worked mold steel by cathodic arc ion plating （CAIP）. The morphologies, phase compositions, and nanoindcntation parameters, such as creep hardness, elastic modulus and plastic de- formation energy of the coatings were analyzed with field emission scanning electron microscopy （FESEM）, X-ray diffraction （XRD） and nanoindentation testing, respectively, and the test results were compared with equation describing the indentation model. The results show that the TiN, TiA1N and TiAISiN coating surfaces were dense and composed of TiN, TiN ＋ TiA1N, TiN ＋ Si3N4 ＋ TiAIN phases, respectively. There was no spalling or cracking on the indentation surface. The creep hardness of the TiN, TiA1N and TiAISiN coatings was 7.33, 13.5, and 15.2 GPa, respectively; the corresponding hardness measured by nanoindentation was 7.09, 15.6, and 21.7 GPa, respectively; and the corresponding elastic modulus was 201.93, 172.79, and 162.77 GPa, respectively. The contact depth and elastic modulus calculated by the indentation model were close to those of the test results, but the remaining indentation parameters showed discrepancies. The sequence of plastic deformation energy was TiN 〉 TiA1N〉TiAISiN.