Deformation, Phase Transformation and Recrystallization in the Shear Bands Induced by High-Strain Rate Loading in Titanium and Its Alloys

α-titanium and its alloys with a dual-phase structure （α＋β） were deformed dynamically under strain rate of about 10^4 s^-1. The formation and microstructural evolution of the localized shear bands were characterized by scanning electron microscopy （SEM） and transmission electron microscopy （TEM）. The results reveal that both the strain and strain rate should be considered simultaneously as the mechanical conditions for shear band formation, and twinning is an important mode of deformation. Both experimental and calculation show that the materials within the bands underwent a superhigh strain rate （9×10^5 S^-1） deformation, which is two magnitudes of that of average strain rate required for shear band formation; the dislocations in the bands can be constricted and developed into cell structures; the phase transformation from α to α2 within the bands was observed, and the transformation products （α2） had a certain crystallographic orientation relationship with their parent; the equiaxed grains with an average size of 10 μm in diameter observed within the bands are proposed to be the results of recrystallization.

TEM OBSERVATION OF LOCAL DEFORMATION BAND AT CRACK TIP

The thin foil specimen of a ferrite-austenite duplex stainless steel was tensiled under transmis- sion electron microscope(TEM).It was found that both in ferrite and austenite the local deformation band at crack tip was formed near to the crack propagating direction.Its forma- tion was related with the crack tip Schmid factor,dislocation shielding,latent hardening and hardening coefficient.When the crack tip emitted dislocations to a slip system by the action of pure mode Ⅱ stress resolute,and the decreasing rate of hardening coefficient was suitable,lo- cal deformation band was easy to form.

DEFORMATION LOCALIZATION AND SHEAR BAND FRACTURE IN STRONG ANISOTROPY SHEET TENSION

The tensile deformation localization and the shear band fracture behaviors of sheet metals with strong anisotropy are numerically simulated by using Updating Lagrange finite element method, Quasi-how plastic constitutive theory([1]) and B-L planar anisotropy yield criterion([2]). Simulated results are compared with experimental ones. Very good consistence is obtained between numerical and experimental results. The relationship between the anisotropy coefficient R and the shear band angle theta is found.

Numerical simulation of shear band localization in geotechnical materials based on a nonlocal plasticity model

A new nonlocal plasticity model,which is based on the integral-type nonlocal model and the cubic representative volumetric element（RVE）,is proposed to simulate shear band localization in geotechnical materials such as soils and rocks.An algorithm is developed to solve the resulting nonlinear system of equations.In this algorithm,the nonlocal averaging of plastic strain over the RVE is evaluated using C0 elements instead of using C1 elements to solve the second-order gradient of plastic strains.To obtain the average plastic strain,a set of special elements,called the nonlocal elements,are constructed to approximate the RVE.The updating of average stresses of the local element is based on the nonlocal plastic strain of the corresponding nonlocal elements.Numerical examples show that meshindependent results can be achieved using the proposed model and the algorithm,and the thickness of the shear band is insensitive to the mesh refinement.

Flat band localization due to self-localized orbital

We discover a new wave localization mechanism in a periodic wave system,which can produce a novel type of flat band and is distinct from the known localization mechanisms,i.e.,Anderson localization and flat band lattices.The first example we give is a designed electron waveguide(EWG)on 2DEG with special periodic confinement potential.Numerical calculations show that,with proper confinement geometry,electrons can be completely localized in an open waveguide.We interpret this flat band localization(FBL)phenomenon by introducing the concept of self-localized orbitals.Essentially,each unit cell of the waveguide is equivalent to an artificial atom,where the self-localized orbital is a special eigenstate with unique spatial distribution.These self-localized orbitals form the flat bands in the waveguide.Such self-localized orbital induced FBL is a general phenomenon of wave motion,which can arise in any wave systems with carefully engineered boundary conditions.We then design a metallic waveguide(MWG)array to illustrate that similar FBL can be readily realized and observed with electromagnetic waves.

Failure characteristics of three-body model composed of rock and coal with different strength and stiffness

Four different types of three-body model composed of rock and coal with different strength and stiffness were established in order to study the failure characteristics of compound model such as roof-coal-floor. Through stress analysis of the element with variable strength and stiffness extracted from the strong-weak interface, the tri-axial compressive strength of the weak body and strong body near the interface as well as the areas away from the contact surface was found. Then, on the basis of three-dimensional fast Lagrangian method of continua and strain softening constitutive model composed of Coulomb-Mohr shear failure with tensile cut-off, stress and strain relationship of the four three-body combined models were analyzed under different confining pressures by numerical simulation. Finally, the different features of local shear zones and plastic failure areas of the four different models and their development trend with increasing confining pressure were discussed. The results show that additional stresses are derived due to the lateral deformation constraints near the strong-weak interface area, which results in the strength increasing in weak body and strength decreasing in strong body. The weakly consolidated soft rock and coal cementation exhibit significant strain softening behavior and bear compound tension-shear failure under uni-axial compression. With the increase of confining pressure, the tensile failure disappears from the model, and the failure type of composed model changes to local shear failure with different number of shearing bands and plastic failure zones. This work shows important guiding significance for the mechanism study of seismic, rock burst, and coal bump.

An approach to evaluate ground surface rupture caused by reverse fault movement

An approach for estimating ground surface rupture caused by strong earthquakes is presented in this paper, where the finite element （FE） method of continuous and discontinuous coalescent displacement fields is adopted. The onset condition of strain localization is introduced to detect the formation of the slippage line. In the analysis, the Drucker-Prager constitutive model is used for soils and the rate- and state-dependent friction law is used on the slippage line to simulate the evolution of the sliding. A simple application to evaluate the ground surface rupture induced by a reverse fault movement is provided, and the numerical simulation shows good agreement with failure characteristics observed in the field after strong earthquakes.

Numerical and Experimental Investigations on Tunable Low-frequency Locally Resonant Metamaterials

In this paper,a tunable locally resonant metamaterial is proposed for low-frequency band gaps.The local resonator composed of two pairs of folded slender beams and a proof mass is designed based on the theory of compliant mechanism.The design optimization on geometric parameters is carried out to fulfil the quasi-zero-stiffness property.The locally resonant metamaterial is formed by periodically arranged unit cells,and the transmittance of longitudinal wave is studied through three aspects:numerical predictions,finite element simulations and experimental tests.The variation trends revealed by these three methods match well with one another:the band gap moves to lower frequency and both its depth and width get smaller and smaller with the increase of pre-compression(Δ).The band gap overlays the frequency range of 73.10–92.38 Hz and 16.78–19.49 Hz atΔ=0mm andΔ=10mm,respectively,providing a wide range of tunability.Besides,the ultralow-frequency band gap can be achieved asΔapproaches 10 mm.This study may provide an avenue for achieving the tunable ultralow-frequency locally resonant band gap.