Experimental and Numerical Analysis of Forming Limit Diagram (FLD) and Forming Limit Stress Diagram (FLSD)

In this work, forming limit diagram for aluminum alloy 3105 is performed experimentally and forming limit based on stress (FLSD) calculated from strains that resulted from experimental procedure. In addition, numerical prediction by ductile fracture criteria using simulation is considered and it is shown that they are well suited with the experimental results. The strain paths from finite element simulations are found fairly acceptable to represent both sides of the FLD.

Forming Limit Stress Diagram Prediction of Aluminum Alloy 5052 Based on GTN Model Parameters Determined by In Situ Tensile Test

The conventional forming limit diagram （FLD） is described as a plot of major strain versus minor strain. However, FLD is dependent on forming history and strain path. In the present study, a forming limit stress-based diagram （FLSD） has been adopted to predict the fracture limit of aluminum alloy （AA） 5052-O1 sheet. Nakazima test is simulated by plastic constitutive formula derived from the modified Gurson-Tvergaard-Needleman （GTN） model. An in situ tensile test with scanning electron microscope （SEM） is proposed to determine the parameters in GTN model. The damage evolution is observed and recorded, and the parameters of GTN model are identified through counting void fraction at three damage stages of AA5052-O 1. According to the experimental results, the original void volume fraction, the volume fraction of potential nucleated voids, the critical void volume fraction, the void volume fraction at the final failure of material are assigned as 0.002 918, 0.024 9, 0.030 103, 0.048 54, respectively. The stress and strain are obtained at the last loading step before crack. FLSD and FLD of AA5052-O 1 are plotted. Compared with the experimental Nakazima test and uniaxial tensile test, the predicted results show a good agreement. The parameters determined by in situ tensile test can be applied to the research of the forming limit for ductile metals.

Proportional Limit Stress and Residual Thermal Stress of 3D SiC/SiC Composite

Proportional limit stress （PLS） and residual thermal stresses （RTS） of 3D SiC/SiC composite were investigated. PLS was obtained by four different methods from the monotonic stress-strain response curve to get a convincing value. RTS in the SiC matrix was quantified by solving the geometric intersection point of the regression lines of hysteresis loops from the periodical loading-unloading-reloading cycle test curve. Classical ACK model and analytical formulas were used to analytically calculate the PLS and RTS of 3D SiC/ SiC composite. Good agreement between the experimental results and the analytical calculation was observed. And relationship between the PLS and the RTS of 3D SiC/SiC was discussed.

Stress based forming limit diagram for formability characterization of 6061 aluminum

Two numerical criteria of forming limit diagram（FLD） criterion and ductile fracture criterion（DFC） are presented for FLD prediction of 6061 aluminum. The numerical results are compared with the experimental FLD and also punch＇s load-displacement curve of experimental samples. Experimental FLD of this study is calculated using hemispherical punch test of Hecker. Experimental FLD is converted to FLSD and imported to the Abaqus software to predict necking of samples. Numerical results for FLSD prediction were compared with experimental FLSD. Results show that ductile fracture criterion has higher accuracy for FLD and FLSD prediction of 6061 aluminum. Comparison of numerical and experimental results for force-displacement curve of punch shows that numerical results have a good agreement with experiment.

Determination and application of stress-based forming limit diagram in aluminum tube hydroforming

The stress-based forming limit diagram(FLSD) established with limit stress is independent of the strain paths. Compared with traditional strain-based forming limit diagram(FLD),it is more convenient and practical to use as the criterion of forming limit under complex strain paths. The forming limit of 3A21 aluminum alloy sheet was tested and its forming limit diagram(FLD) was determined. Then the FLSD of 3A21 was constituted by transformation formulas between limit strain and limit stress. This FLSD was used in conjunction with LS-DYNA finite element simulations to predict the onset of fracture and limit forming pressure in tube hydroforming. The results indicate that the fracture often occurs in the transition region between corner and straight side of the tube,and the limit forming pressure is 46.4 MPa. The simulation result agrees with the experimental result,and the FLSD is able to predict the forming limit of tube hydroforming with remarkable accuracy.

Mechanism of energy limit equilibrium of rock burst in coal mine

With the increase of mining depth,the effect of rock burst on coal mining is becoming more and more obvious and the rock burst mechanism becomes more and more complicated.Scholars from many countries had put forward different mechanisms,but no one gave a reasonable explanation to the mechanism of rock burst.In this paper,based on the energy theories,we studied the energy limit equilibrium（ELE） of coal mine rock burst The coal seam with rock burst is divided into energy limit equilibrium zone（ELEZ）（A） and elastic zone（B）;we also determined the position where the rock burst occurs,including the roof and floor of coal seams;in addition,we derived the limit width of ELEZ and the mathematic relationship between the limit width and occurrence mechanism of rock burst：the energy difference function（EDF）,w（x） = w_j - w_p,because first-order derivative w＇（x）,is less than 0.So EDF is a monotonically decreasing function.The graph of the energy difference function was also determined, through which we analysed the occurrence mechanism of rock burst.

LIMIT EQUILIBRIUM STATE OF ISOTROPIC ROCKS AROUND THE TUNNEL OUTLINE

The assumed presupposition of limit equilibrium theory is recounted. Based on this, the expressive formula of radius of the non-elastic zone and rock displacement of tunnel outline was given.

Thermal-stress induced phenomena in two-component material:part I

The paper deals with analytical fracture mechanics to consider elastic thermal stresses acting in an isotropic multi-particle-matrix system. The multi-particle-matrix system consists of periodically distributed spherical particles in an infinite matrix. The thermal stresses originate during a cooling process as a consequence of the difference αm - αp in thermal expansion coefficients between the matrix and the particle, αm and αp, respectively. The multi-particle-matrix system thus represents a model system applicable to a real two-component material of a precipitation-matrix type. The infinite matrix is imaginarily divided into identical cubic cells. Each of the cubic cells with the dimension d contains a central spherical particle with the radius R, where d thus corresponds to inter-particle distance. The parameters R, d along with the particle volume fraction v = v（R, d） as a function of R, d represent microstructural characteristics of a twocomponent material. The thermal stresses are investigated within the cubic cell, and accordingly are functions of the microstructural characteristics. The analytical fracture mechanics includes an analytical analysis of the crack initiation and consequently the crack propagation both considered for the spherical particle （q = p） and the cell matrix （q = m）. The analytical analysis is based on the determination of the curve integral Wcq of the thermal-stress induced elastic energy density Wq. The crack initiation is represented by the determination of the critical particle radius Rqc = Rqc（V）. Formulae for Rqc are valid for any two-component mate- rial of a precipitate-matrix type. The crack propagation for R 〉 Rqc is represented by the determination of the function fq describing a shape of the crack in a plane perpendicular

Water Deficit Stress Effects on Corn (<i>Zea mays</i>, L.) Root:Shoot Ratio

A study was conducted at Akron, CO, USA, on a Weld silt loam in 2004 to quantify the effects of water deficit stress on corn (Zea mays, L.) root and shoot biomass. Corn plants were grown under a range of soil bulk density and water conditions caused by previous tillage, crop rotation, and irrigation management. Water deficit stress (Dstress) was quantified by the number of days when the water content in the surface 0.3 m deviated from the water content range determined by the Least Limiting Water Range (LLWR). Root and shoot samples were collected at the V6, V12, and R1 growth stages. There was no significant correlation between Dstress and shoot or root biomass at the V6 growth stage. At the V12 and R1 growth stages, there were negative, linear correlations among Dstress and both root biomass and shoot biomass. The proportional decrease of shoot biomass was greater than the proportional decrease in root biomass, leading to an increase in the root:shoot ratio as water deficit stress increased at all growth stages. Determining restrictive soil conditions using the LLWR may be useful for evaluating improvement or degradation of the soil physical environment caused by soil management.

Fatigue Limit Prediction and Estimation for the Crack Size Rendered Harmless by Peening for Welded Joint Containing a Surface Crack

In this study, the effects of portable pneumatic needle-peening (PPP) on the bending fatigue limit of a low-carbon steel SM490A welded joint containing a semi-circular slit on the weld toe were investigated. PPP was applied to the specimens with a semi-circular slit with depths of a = 0.4, 0.8, 1.2, and 1.6 mm. Then, three-point bending fatigue tests were carried out under R = 0.05. The fatigue limits of low-carbon steel welded specimens containing a semi-circular slit were increased for peened specimens compared with non-peened specimens. Peened specimens having a semicircular slit with a depth of a = 1.2 mm had high fatigue limits, almost equal to those of the non-slit peened specimens. It was concluded that a semi-circular slit with a depth of less than a = 1.2 mm can be rendered harmless by peening. Then, the fatigue improvement by peening was predicted. The fatigue limits before and after peening could be estimated accurately by using a modified Goodman diagram considering the effects of residual stress, stress concentration, and Vickers hardness. Moreover, the maximum depth of a semi-circular slit that can be rendered harmless by PPP was estimated based on fracture mechanics assuming that the semi-circular slit was equivalent to a semi-circular crack. The prediction results were almost consistent with the experimental results.

LOWER BOUND LIMIT ANALYSIS OF THREE-DIMENSIONAL ELASTOPLASTIC STRUCTURES BY BOUNDARY ELEMENT METHOD

Based on the lower bound theorem of limit analysis, a solution procedure for limit analysis of three_dimensional elastoplastic structures was established using conventional boundary element method (BEM). The elastic stress field for lower bound limit analysis was computed directly by three_dimensional boundary element method (3_D BEM). The self_equilibrium stress field was constructed by the linear combination of several self_equilibrium “basis vectors” which can be computed by elastic_plastic incremental iteration of 3_D BEM analysis. The lower bound limit analysis problem was finally reduced to a series of nonlinear programming sub_problems with relatively few optimal variables. The complex method was used to solve the nonlinear programming sub_problems. The numerical results show that the present solution procedure has good accuracy and high efficiency.

A SOLUTION PROCEDURE FOR LOWER BOUND LIMIT AND SHAKEDOWN ANALYSIS BY SGBEM

The symmetric Galerkin boundary element method (SGBEM) instead ofthe finite element method is used t perform lower bound limit andshakedown analysis of structures. The self-equilibrium stress fieldsare constructed by a linear combination of several basicself-equilibrium stress fields with parameters to be determined.These basic self-equilibrium stress fields are expressed as elasticresponses of the body to im- posed permanent strains and obtainedthrough elastic-plastic incremental analysis.

Analytic Solution of Elasto-Plastic Stress in Infinite Slope under Uniform Load

According to the Mohr-Coulomb yield criterion, the stress field of the infinite slope is derived under a vertical uniform load q on the top of the slope. It is indicated that elastic and elasto-plastic states would occur in the slope. When q is smaller than the critical load, q(p), the slope is in the elastic state. If q equals q(p), the slope is in the critical state, and the plastic deformation would occur along the critical angle. With the increase of q, the plastic zone would extend, and the slope is in the elasto-plastic State. If q equals limit load, the slope is in the limit equilibrium state. The slope may be divided into three zones. Some charts of the critical angle, the critical and limit load coefficients are presented in this paper.

INFLUENCE OF RESIDUAL STRESS AND SURFACE MORPHOLOGY ON FATIGUE PROPERTIES OF STEEL 60Mn

Influence of residual stress and surface morphology induced by shot-peening on fatigue behav- ior of a medium temperature tempered spring steel 60 Mn has been studied.The compressive residual stress induced in the near-surface region may improve fatigue limit from 930 to 1010 MPa,and the very high tensile residual stress in the interior may reduce it from 1010 to 940 MPa,whereas the severe surface damage may cause a drop-off of it from 1010 down to 800 MPa.Fatigue cracks initiated in such position where the equivalent Mises stress,including residual stress,exceeded the local strength of the material.The compressive residual stress, induced by shot-peening,may intensify the effect of crack closure,so as to decrease the crack growth rate.

A novel limiting strain energy strength theory

With applied dislocation theory,the effects of shear and normal stresses on the slide and climb motions at the same section of a crystal were analyzed.And,based on the synergetic effect of both normal and shear strain specific energies,the concept of the total equivalent strain specific energy(TESSE)at an oblique section and a new strength theory named as limiting strain energy strength theory(LSEST)were proposed.As for isotropic materials,the plastic yielding or brittle fracture of under uniaxial stress state would occur when the maximum TESSE reached the strain specific energy,also the expressions on the equivalent stresses and a function of failure of the LSEST under different principal stress states were obtained.Relationship formulas among the tensile, compressive and shear yield strengths for plastic metals were derived.These theoretical predictions,according to the LSEST,were consistent very well with experiment results of tensile,compressive and torsion tests of three plastic metals and other experiment results from open literatures.This novel LSEST might also help for strength calculation of other materials.

Study on the high-temperature properties of heat-resistant steel 309S

The properties of heat-resistant steel 309S at elevated properties were investigated.The results revealed a rapid decrease in the short-time tensile strength at elevated temperatures.At 1 000 ℃,the yield strength and tensile strength are 14% and 7% of their respective values at room temperature,respectively.The creep rupture strength was inferred in terms of the relationship between stress and duration time at high temperatures.After 1 000 h,the creep rupture strength is 37.98 MPa at 800 ℃,12.63 MPa at 900 ℃,and 7.27 MPa at 1 000 ℃.The fractures occurring at these high temperatures were intergranular in nature.Under the experimental condition,the fatigue limit stress is 25 MPa.The number of fatigue cycles and crack growth time decrease with increasing stress.Fracture morphology analysis shows that the fatigue cracks initiate on the surface of the sample and propagate through transgranular expansion.

锥面分段开孔高速刀柄的设计方法

根据高速刀柄在不同过盈量下的联接性能分析结果与不同转速下的锥面接触应力分布规律,提出了一种锥面分段开孔高速刀柄的设计方法,即对刀柄定位锥面按照锥体素线长度均等分成前、中、后三段,并在各段的中等分处周向均布一组盲孔,通过调控盲孔的数量与尺寸使刀柄锥面达到一定的柔度。文章阐述了盲孔开设参数对锥面接触应力、柔度的影响规律和参数确定原则,给出了以HSK-E50为原型的锥面分段开孔设计案例,采用有限元分析其极限转速和锥面接触应力分布情况。结果表明,锥面分段开孔刀柄与原型刀柄相比,极限转速提高了约10.79%,锥面接触应力分布显著均匀。

基于有限单元法驾驶室防翻保护结构性能分析

防滚翻保护装置(ROPS)设计的可靠性,直接影响驾驶员是否能得到有效的保护。根据实车尺寸和视野要求,进行ROPS结构设计和挠曲极限量DLV设计;利用UG建立驾驶室三维模型,并建立有限元分析模型;根据国家标准关于ROPS的规定,对驾驶室翻滚保护的安全性进行分析,重点对不同方向的承载进行分析;基于驾驶室翻滚测试试验台,选取侧向加载进行测试,验证模型分析的可靠性。结果可知:当侧向力增加到140kN时,驾驶室吸收的能量为16672J,满足最小能量吸收能力要求;侧向载荷加载时,应力和位移均出现最大值,分别为372MPa和11.86mm,满足材料承载和能量加载要求;试验获得侧向加载时的最大应力和最大位移,满足材料和设计尺寸的要求,且与仿真结果的误差均小于4%,表明仿真分析模型是可靠的。所设计的防翻保护装置可以起到保护作用,为此类设计生产提供参考。

考虑硬化历史的圆筒形件二次拉深极限拉深比的解析模型

以圆筒形件二次拉深成形为例,基于主应力法和板料弯曲理论,考虑材料硬化历史、壁厚比t_(min)/t_(max)、凹模圆角半径和摩擦因数的影响,建立了一种预测圆筒形件二次拉深极限拉深比的解析模型,并对SUS304不锈钢板料进行了拉深试验验证。结果表明:解析模型的预测值与试验结果吻合较好;考虑硬化历史的解析模型与未考虑硬化历史的模型相比二次拉深极限拉深比相差约10%;摩擦因数、凹模圆角半径对二次拉深极限拉深比有显著影响,摩擦因数越大,二次拉深极限拉深比越小;凹模圆角半径越大,二次拉深极限拉深比越大。

峰前峰后循环加卸载对砂岩动力特性的影响

为深入分析砂岩峰前和峰后不同阶段的动力特性规律,开展单轴分级循环加卸载试验,综合分析下限应力对砂岩峰前峰后不同加卸载阶段的表观弹性模量、滞回圈面积、阻尼比、阻尼系数及动弹性模量等相关动力参数的影响。研究结果表明:①岩样在峰后因内部损伤加深和累积,相同下限应力下滞回曲线位于峰前右侧,且应变量增幅和最大应变增幅均随下限应力的增加而逐渐减小,说明峰后岩样虽然强度已达到极限状态,但只要岩石未完全破坏失稳,其致密性仍可以在高应力条件下的循环加卸载中得到增强。②砂岩在峰前峰后循环加卸载下的变化过程,可以通过表观弹性模量曲线斜率a值的变化得以体现,低下限应力循环加卸载试验中,致密性增强系数a_(1)>致密性劣化系数a_(2),斜率a均为正值,轴向应力对岩石整体的压密作用明显强于劣化损伤作用;随着下限应力升高,a_(2)的降低速率高于a_(1)的升高速率,a值逐渐减小甚至变为负值,说明轴向应力对岩石整体的压密作用逐渐弱于劣化损伤作用。③4组不同下限应力条件下,岩样峰后的滞回圈面积、阻尼比、阻尼系数均高于峰前状态,而动弹性模量低于峰前状态,说明岩样在峰后循环加卸载过程中内部劣化损伤程度高于峰前。