Residual elastic stress strain field and geometrically necessary dislocation density distribution around nano-indentation in TA15 titanium alloy

Nanoindentation and high resolution electron backscatter diffraction（EBSD） were combined to examine the elastic modulus and hardness of α and β phases,anisotropy in residual elastic stress strain fields and distributions of geometrically necessary dislocation（GND） density around the indentations within TA15 titanium alloy.The nano-indention tests were conducted on α and β phases,respectively.The residual stress strain fields surrounding the indentation were calculated through crosscorrelation method from recorded patterns.The GND density distribution around the indentation was calculated based on the strain gradient theories to reveal the micro-mechanism of plastic deformation.The results indicate that the elastic modulus and hardness for α p hase are 129.05 GPas and 6.44 GPa,while for β phase,their values are 109.80 GPa and 4.29 GPa,respectively.The residual Mises stress distribution around the indentation is relatively heterogeneous and significantly influenced by neighboring soft β phase.The region with low residual stress around the indentation is accompanied with markedly high a type and prismatic-GND density.

EFFECT OF THE POISSON RATIO ON THE PERFECTLY PLASTIC STRESS FIELD AT A STATIONARY PLANE-STRAIN CRACK TIP

Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode I, Mode II and Mixed-Mode I-II plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.

Effect of external stress and bias magnetic field on transformation strain of heusler alloy Ni-Mn-Ga

The influence of external field(magnetic field and stress field) on the transformation strain of Ni 52.9- Mn 24.4Ga 22.7 single crystal were investigated and its mechanism was also discussed. When thermally martensitic transformation occurs, about 0.25% transformation strain is obtained which may be obviously enhanced to about 0.8% by a 6 000 Oe magnetic bias field. However, the strain decreases by the external compress stress loaded along the strain-measured direction. When the external compress stress and bias magnetic field are simultaneously applied, the transformation strain decreases with increasing the magnetic field, which is related to the rearrangement of the martensite variants influenced by the external field.

Characteristics of present-day active strain field of Chinese mainland

On the basis of the GPS data obtained from repeated measurements carried out in 2004 and 2007,the horizontal principal strain of the Chinese mainland is calculated,which shows that the direction of principal compressive strain axis of each subplate is basically consistent with the P-axis of focal mechanism solution and the principal compressive stress axis acquired by geological method.It indicates that the crustal tectonic stress field is relatively stable in regions in a long time.The principal compressive stress axes of Qinghai-Tibet and Xinjiang subplates in the western part of Chinese mainland direct to NS and NNE-SSW,which are controlled by the force from the col-lision of the Eurasia Plate and India Plate.The principal compressive strain axes of Heilongjiang and North China subplates in the eastern part direct to ENE-WSW,which shows that they are subject to the force from the collision and underthrust of the Eurasia Plate to the North America and Pacific plates.At the same time,they are also af-fected by the lateral force from Qinghai-Tibet and Xinjiang subplates.The principal compressive strain axis of South China plate is WNW-ESE,which reflects that it is affected by the force from the collision of Philippine Sea Plate and Eurasia Plate and it is also subject to the lateral force from Qinghai-Tibet subplate.It is apparent from the comparison between the principal compressive strain axes in the periods of 2004～2007 and 2001～2004 that the acting directions of principal compressive stress of subplates in both periods are basically consistent.However,there is certain difference between their directional concentrations of principal compressive stress axes.The sur-face strain rates of different tectonic units in both periods indicate that the events predominating by compressive variation decrease,while the events predominating by tensile change increase.

Elastic Strain Field Distribution of a Self-Organized Growth Lensed-Shaped Quantum Dot by Finite Element Method

The stress and strain fields in self-organized growth coherent quantum dots （QD） structures are investigated in detail by two-dimension and three-dimension finite element analyses for lensed-shaped QDs. The nonobjective isolate quantum dot system is used. The calculated results can he directly used to evaluate the conductive band and valence band confinement potential and strain introduced by the effective mass of the charge carriers in strain QD.

Characteristics of evolution of mining-induced stress field in the longwall panel:insights from physical modeling

The evolution of mining-induced stress field in longwall panel is closely related to the fracture field and the breaking characteristics of strata.Few laboratory experiments have been conducted to investigate the stress field.This study investigated its evolution by constructing a large-scale physical model according to the in situ conditions of the longwall panel.Theoretical analysis was used to reveal the mechanism of stress distribution in the overburden.The modelling results showed that:(1)The major principal stress field is arch-shaped,and the strata overlying both the solid zones and gob constitute a series of coordinated load-bearing structures.The stress increasing zone is like a macro stress arch.High stress is especially concentrated on both shoulders of the arch-shaped structure.The stress concentration of the solid zone in front of the gob is higher than the rear solid zone.(2)The characteristics of the vertical stress field in different regions are significantly different.Stress decreases in the zone above the gob and increases in solid zones on both sides of it.The mechanical analysis show that for a given stratum,the trajectories of principal stress are arch-shaped or inverselyarched,referred to as the‘‘principal stress arch’’,irrespective of its initial breaking or periodic breaking,and determines the fracture morphology.That is,the trajectories of tensile principal stress are inversely arched before the first breaking of the strata,and cause the breaking lines to resemble an inverted funnel.In case of periodic breaking,the breaking line forms an obtuse angle with the advancing direction of the panel.Good agreement was obtained between the results of physical modeling and the theoretical analysis.

Numerical simulation study on the influence of the ground stress field on the stability of roadways

We adopt the concept of generalized plane strain to model a roadway in a stress field.This can avoid limitations caused by simplifying the stress analysis as plane strain.FLAC3D was used to investigate the maximum tensile stress and displacement of a roadway in a known stress field for angles,α,between the roadway axial direction and the maximum principal stress of 0°,30°,45°,60° and 90°.This theory was applied to the analysis of an engineering case.The results indicate that stress and displacement of the surrounding rock increase as the angle,α,increases.This provides some significant guidance for a reasonable layout of roadways in a known stress field.

MODE Ⅰ CRACK TIP FIELD WITH STRAIN GRADIENT EFFECTS

A plane strain mode 1 crack tip field with strain gradient effects is investigated.A new strain gradient theory is used.An elastic-power law hardening strain gradient material is considered and two hardening laws,i.e.a separation law and an integration law are used respectively.As for the material with the separation law hardening,the angular distributions of stresses are consistent with the HRR field,which differs from the stress results;the angular distributions of couple stresses are the same as the couple stress results.For the material with the integration law hardening,the stress field and the couple stress field can not exist simultaneously,which is the same as the conclusion,but for the stress dominated field,the an- gular distributions of stresses are consistent with the HRR field;for the couple stress dominated field,the an- gular distributions of couple stresses are consistent with those in Ref.However,the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only,while the crack tip field of mode 1 is dominated by the tension gradient,which will be shown in another paper.

Stress/strain distributions for weld metal solidification crack instain less steels

This paper has simulated the driving force of solidification crack of stainless steels, that is, stress/strain field in the trail of molten pool. Firstly, the effect of the deformation in the molten pool was eliminated after the element rebirth method was adopted. Secondly, the influence of solidification shrinkage was taken into account by increasing thermal expansion coefficients of the steels at elevated temperatures. Finally, the stress/strain distributions of different conditions have been computed and analyzed. Furthermore, the driving force curves of the solidification crack of the steels have been obtained by converting strain time curves into strain temperature curves, which founds a basis for predicting welding solidification crack.

NUMERICAL SIMULATION OF STRESS-STRAIN DISTRIBUTIONS FOR WELD METAL SOLIDIFICATION CRACKING IN STAINLESS STEEL

This paper analyzed the characteristics of welding solidification crack of stainless steels,and clearly re- vealed the the of the deformation in the molten - the pool and the solidification shrinkage on the stress - strain fields in the trail of molten - weld pool.Moreover, rheologic properties of the alloys in solid - liquid zone were also obtained by measuring the hading and unloading deform curves of the steels.As a result, a numerical model for simulation of stress - strain distributions of welding solidifi- cation crack was developed. On the basis of the model,the thesis simulated the driving force of solidifi- cation crack of stainless steels, that is, stress - strain fields in the trail of molten-weld pool with fi- nite element method.

MODE Ⅰ AND MODE Ⅱ CRACK TIP ASYMPTOTIC FIELDS WITH STRAIN GRADIENT EFFECTS

The strain gradient effect becomes significant when the size of frac- ture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dom- inant strain field is irrotational. For mode Ⅰ plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist si- multaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode Ⅱ plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode Ⅱ plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode Ⅰ and mode Ⅱ, because the present theory is based only on the rotational gradi- ent of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

Stress-strain characteristics of linear friction welding of TC11 and TC17 alloys

Abstract Transient stress and strain fields of dissimilar titanium alloys （TCll and TC17 ） joint during linear friction welding （ LFW） were investigated by a two-dimensional model with ABAQUS/Explicit. The results showed that in the X-axis, the maximum compressive stress of 850 MPa occurred in the center zone of friction interface , and the maximum tensile stress of 190 MPa distributed at the flash; in the Y-axis, the maximum compressive stress of 1 261 MPa located at the junction region between the welding fixture and edge of the specimen, and the maximum tensile stress of 320 MPa distributed in the connecting portion between the flash and edge of the specimen. In addition, areas of plastic strain increased gradually during welding process. In the X-axis, tensile strain mainly existed at the heads of the specimens; in the Y-axis, compressive strain mainly occurred at the heads of the specimens.

THE EXPRESSION OF STRESS AND STRAIN AT THE TIP OF NOTCH IN REISSNER PLATE

In this paper, the eigenequation of notch in Reissner plate is derived by the eigenfunction method. Eigenvalues of different notches with different angles are calculated by Muller iteration method. The expression of stress and strain at the tip of notch in Reissner plate is obtained.

Interaction among fractures and stress field computation of fracture systems

The interaction problem among fractures under the action of compressional stress is studied in this paper by using the finite element method and boundary element method respectively.The mechanical criteria which differentiate between the independent fractures and fracture systems and their computation methods are presented in this paper.The proportional conditions between length and spacing of fractures that exist interaction for several kinds of fracture groups of different geometric arrangement are given.The effect of interaction among fractures on the displacement field,stress field and strain energy distribution are computed.The relations between the fracture system of conjugate array and conjugate earthquakes are also discussed in this paper.

Formulation and procedure for in situ stress back-analysis from borehole strain changes measured during nearby underground excavation

Estimation of in situ stresses based on back-analysis of measured stress changes and displacements has become an alternative to the direct stress measurement methods.In order to help users conduct own measurement and analysis,this paper presents in detail a field stress back-analysis approach directly from borehole strain changes measured during nearby underground excavation.Essential formulations in major steps and the procedure for the entire analysis process are provided to allow users to follow.The instrument for borehole strain change measurement can be the CSIR or CSIRO stress cells and other borehole strain cells that can measure strains on borehole walls.Strain changes corresponding to the stress changes at a borehole location are calculated in borehole environment.The stress changes due to nearby excavation can be calculated by an analytical model for a single circular opening and simulated by a numerical model for non-circular and multiple openings.These models are based on isotropic,homogeneous and linear elastic assumptions.The analysis of borehole strain changes is accomplished by multiple linear regression based on error minimization and an integrated process provides the best-fit solution directly to the in situ stresses.A statistical technique is adopted for screening outliers in the measurement data,checking measurement compatibility and evaluating the reliability of analysis results.An application example is included to demonstrate the practical application and the analysis procedure.

The Expression of Stress and Strain at the Tip of Three-Dimensional Notch

The singularity of stress and strain at the tip of three-dimensional notch isanalysed by the power expansion method .the eigenquation of the notch is gainedthrough the boundary conditions of the notch, the eigenvalues under different innerangles of the notch are obtained, the expression of stress and strain at the tip of thenotch is finally derived .

鄂尔多斯块体及其周缘现今地壳水平形变特征及应力应变耦合关系

针对鄂尔多斯块体地壳变形性质量化研究不足和应力应变耦合关系尚不明确的问题,采用球坐标最小二乘配置模型解算研究区域地壳的特征应变场,利用震源机制解数据反演区域地壳的主应力分布。结果显示,地壳变形主要集中在板块边界带和断陷盆地内,鄂尔多斯块体内部的地壳形变较小。其中,青藏高原东北缘与阿拉善块体的交界处地壳变形尤其剧烈,表现为沿板块边界的强压缩变形,主要变形机制为NW-SE向压缩与NE-SW向弱拉张共存,最大主压应变率超过0.05μstrain。研究区域地壳处于较为统一的张应力环境,最大主应力方向接近水平并指向SEE向,与对应区域的主张应变方向吻合,最小主应力方向更接近主压应变方向。

Characteristics and implications of stress state in a gold mine in Ludong area, China

In this study, we obtained information from twenty-one measurement points on the stress magnitudes and orientations of a gold mine in the Ludong area. We used the overcoring technique with an improved hollow inclusion strain gauge and then analyzed the distribution characteristics of the in situ stress field. The results indicate that the stress field is characterized by σH > σh > σv and σH > σv > σh(where σH, σh, and σv are the maximum horizontal, minimum horizontal, and vertical principal stresses, respectively). The regional stress field is dominated by horizontal principal stress. The σH, σh, and σv values show a gradual increasing trend with depth. The σH is predominantly oriented in the NWW–SEE or near-EW direction. We also confirmed the correspondence between the measured stress field and the regional geological structure. In addition, based on the measured stress data, we discuss the implications of the in situ stress with respect to fault activity in the mine area.

Residual stress modeling of thin wall by laser cladding forming

The residual stress generated in the laser cladding could lead to undesirable distortions or even crack formation. In order to better understand the evolution/yielding process of stress field,a 3 D finite-element thermo-mechanical model was established for the laser cladding formation of thin wall with the 17-4 PH powder on the FV520( B) steel. The temperature field was firstly analyzed,based on which the stress field and strain field of the laser cladding forming process were analyzed.In order to validate the prediction,the final residual stress field in the obtained thin wall was tested by X-ray diffraction in comparison with the predicted results.

Comparative Analysis of Cave Strain and Borehole Bulk Strain of the Tai an Seismic Station

Based on the cave strain observation data in 2013 at Tai'an seismic station,we use the Venedikov harmonic analysis method to calculate the cave strain measurement and phase lag of the tide factor, and qualitatively evaluate the stability of the tidal factor for observational data evaluation. At the same time, the two measurement items of the observation instrument are calculated,and the correlation strain parameters are extracted and compared. On this basis,the strain parameter time series calculation is carried out on the data quality of Taian seismic station,which is relatively stable,and the 2 sets of instruments are compared. Through the analysis, it is found that the stress field is abnormal,and the corresponding relationship between the anomaly of the stress field and the gravity field is compared and analyzed.