Slip-line field solutions of three-point bend specimens with deep notches

Slip-line field solutions of three-point bend specimens with different notch depths, notch angles and notch root radii are presented. For notch angles less than the critical value the plastic region is localized at the ligament but for larger notch angles the plastic region spreads to the flanks of the notch. It is shown that the critical angle decreases with increasing notch depth and decreasing root radius. Solutions for the constraint factor and maximum hydrostatic stress beneath the notch tip are also obtained as a function of both notch depth and root radius for notch angles above and below the critical value.     

Estimation of fully plastic crack tip stresses from equilibrium of least upper bound circular arcs

This paper presents a simple method to estimate fully plastic crack tip stresses based on the equilibrium condition of the least upper bounds for plane strain deformation fields consisting of rigid-body rotation across a circular arc extending from a crack tip across the remaining ligament. The method is applied to deep, single-edge-cracked specimens under combined bending and tension. For various bending-to-tension ratios, the limit loads and crack tip stresses are estimated from the present method and compared with results from finite element limit analyses. The present method gives impressive results.     

非对称塑料齿轮弯曲应力的解析法计算

介绍了非对称渐开线塑料齿轮弯曲应力解析法的计算公式,根据尼曼实验曲线得出了重合度系数的解析表达式,并推导了齿顶到各特性啮合点的距离公式。通过实例计算了各特性啮合点的齿根弯曲应力,说明了非对称渐开线塑料齿轮比对称塑料齿轮具有更高的承载能力。     

Hardening-softening behaviour of tubular cantilever beams

In the large plastic deformation of a tubular cantilever beam loaded by a force at its tip, the strain hardening of the material tends to increase the load-carrying capacity, while local buckling and cross-sectional ovalization (flattening) occurring in the neighbourhood of the root tends to reduce the moment-carrying capacity and results in structural softening. Experiments were carried out for seamless mild steel tubular cantilevers of radius/thickness ratio ranging from 9 to 20 to explore the development of local buckling and flattening and to examine its influence on the global load-carrying capacity of the beam. A simple theoretical model is proposed to predict the global hardening-softening behaviour of tubular cantilever beams in terms of the material properties and geometric parameters of the tube.     

小范围屈服条件下复合材料裂纹尖端塑性区分析

基于复合材料力学,推导Tsai-Hill强度准则在平面应力和平面应变条件下的一般表达式,得到了小范围屈服条件下,含中心裂纹无限大板Ⅰ型裂纹、Ⅱ型裂纹和Ⅰ/Ⅱ复合型裂纹尖端塑性区的解析解。针对不同裂纹倾角及泊松比 和,对裂尖塑性区进行了计算和分析。结果表明平面应变条件下塑性区范围小于平面应力条件下塑性区范围,参数、和 对复合材料裂尖塑性区范围和形状有明显的影响,不同的参数值得到的塑性区结果差别很大。另外,该解既适用于各向异性复合材料,也适用于各向同性材料。     

基于统一强度理论的断裂准则

基于统一强度理论,在小范围屈服条件下,推导Ⅰ、Ⅱ复合型裂纹裂尖塑性区范围的统一解析解。给出不同拉压比α、泊松比υ、中间主应力影响参数b以及裂纹倾角β下的一族塑性区形状与大小的轨迹,讨论以上参数对裂尖塑性区变化的影响。最后基于裂纹尖端塑性区的解析解,提出了一种复合型裂纹断裂准则,分析了裂纹倾角与初始断裂角的关系。结果表明,该准则预测结果比其它准则更精确,与试验结果吻合得非常好。     

Novel micro-deep-hole drill with variable web thickness and flute width

This study proposes a novel micro-deep-hole drill with variable web thickness and flute width to effectively improve the problem of tool breakage and chip clogging during micro-deep-hole drilling. Firstly, the failure form and failure mechanism of micro-drill are explored by performing drilling experiments, and it is found that the torsion fracture and bending fracture are the main premature failure modes of micro-deep-hole drilling tools. The static simulation analysis of micro-drill is further conducted to investigate the influence of geometric parameters on the stiffness and strength of high-aspect-ratio micro-drill, and the results indicate that the web thickness ratio and flute width have significant effects on drill tip stiffness and spiral groove root strength. To balance the rigidity, strength and chip evacuation capability of micro-deep-hole drilling tools, the new micro-drill with variable web thickness and flute width is developed, supplemented by comparative experiments. The results confirm that the new micro-drill has better chip removal ability, greatly reduces the drilling force, torque, drill tip wear and material peeling phenomenon, and significantly enhances the machining quality of hole wall.     

铝合金板材中心孔裂纹尖端塑性区数值计算

通过有限元对铝合金板材中心孔裂纹尖端处塑性区模拟计算,说明在裂纹尖端产生了较大的塑性区,并相应地计算出塑性区的大小。本文通过有限元模拟2124铝合金板材中心孔裂纹扩展情况。铝合金材料为典型的脆性材料,2124铝合金板材在疲劳加载情况下会先进行弹性形变,达到屈服强度后进行塑性形变。本文对2124铝合金板材进行有限元模拟时,先采用线弹性模型,计算裂纹扩展的应力强度因子,然后采用弹塑性模型,计算裂纹尖端的塑性区大小,从而进一步对裂纹尖端应力强度因子进行修正。在建立有限元模型时,以二维的Ramberg-Os-good（R-O）本构为基础,采用参数化的方式,这样是为了可以更好地对有限元程序进行调试。在有限元网格划分时,由于在相同精度下四边形单元的计算效率是三角形单元的几倍,所以采用四边形单元,提高计算精度。有限元建模时,采用plane42、solid 45和solid 95三种单元,plane42单元用于建立2D网格,solid45单元用于建立3D网格,而solid95单元则是用于引入奇异单元。同时,由于试样模型对称性,所以取1/4模型来进行计算。在计算裂纹尖端应力强度因子及塑性区大小时,采用恒ΔK方式和增ΔK两种加载方式来进行计算。首先在恒ΔK下,计算出相应的应力强度因子,其值和理论值相吻合,同时观察得到的塑性区形状与理论形状相似,计算塑性区尺寸大小,首先证明有限元程序的正确性。进一步有限元模拟计算在增大ΔK情况下不同预裂纹长度下塑性区的变化情况。经过有限元计算得到的塑性区尺寸大小,最后可以近似用经验公式表达。     

二维振动铣削切削厚度及刀尖轨迹数值仿真

通过分析二维振动铣削条件下刀尖运动轨迹特点,利用椭圆方程与旋转矩阵建立了描述刀尖运动轨迹最大轮廓的数学模型,在刀具同一转角下,运用距离间计算公式求得任意转角下的切削厚度值。通过对不同加工参数下刀尖轨迹数值仿真分析,获得了实现理想刀尖轨迹和切削厚度曲线的条件,从而为二维振动铣削的理论研究打下基础。     

Surface roughness modeling in Laser-assisted End Milling of Inconel 718

Inconel 718 is a difficult-to-machine material while products of this material require good surface finish. Therefore, it is essential for the evaluation and prediction of surface roughness of machined Inconel 718 workpiece to be developed. An analytical model for the prediction of surface roughness under laser-assisted end milling of Inconel 718 is proposed based on kinematics of tool movement and elastic response of workpiece. The actual tool trajectory is first predicted with the consideration of overall tool movement, elastic deformation of tool, and the tool tip profile. The tool movements include the translation in feed direction and the rotation along its axis. The elastic deformation is calculated based on the previously established milling force prediction model. The tool tip profile is predicted based on the tool tip radius and angle. The machined surface profile is simulated based on the tool trajectory with elastic recovery, which is considered through the comparison between the minimum thickness and actual cutting thickness. Experiments are conducted in both conventional and laser-assisted milling under seven different sets of cutting parameters. Through the comparison between the analytical predictions and experimental measurements, the proposed model has high accuracy with the maximum error less than 27%, which is more accurate for lower feed rate with error less than 3%. The proposed analytical model is valuable for providing a fast, credible, and physics-based method for the prediction of surface roughness in milling process.     

Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

In the digital image correlation research of fatigue crack growth rate,the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor,thereby affecting the life prediction.This paper proposes a Gauss-Newton iteration method for solving the crack tip position.The conventional linear fitting method provides an iterative initial solution for this method,and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix.A noise-added artificial displacement field is used to verify the feasibility of the method,which shows that all parameters can be solved with satisfactory results.The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result,and the relative error between the two is only-0.621％;The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip,and the maximum relative error with the test plastic zone area is-11.29％.The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05％.The crack tip coordinates,stress intensity factors,and plastic zone contour changes in the loading and unloading phases are explored.The results show that the crack tip change during the loading process is faster than the change during the unloading process;the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process;under the same load,the theoretical plastic zone during the unloading process is higher than that during the loading process.     

Macroscopic and microscopic analysis of the tongue of the common opossum (Didelphis marsupialis)

We performed a macroscopic and microscopic study of the tongues of common opossums, Didelphis marsupialis, from South America. We studied two males and two females. We collected morphometric data on the tongue with precision calipers. For the light microscopy and scanning electron microscopy analyses, we fixed tissue fragments in 10% formaldehyde and 2.5% glutaraldehyde, respectively. The opossum tongues averaged 5.87 ± 0.20 cm in length, 3.27 ± 0.15 cm in width at the lingual body, and 3.82 ± 0.15 cm in width at the root. The mean thickness of the lingual body was 1.8 ± 0.1 cm, and the thickness of the root was 3.82 ± 0.15 cm. Sharp filiform papillae were scattered across the entire tongue; conical filiform papillae occurred on the lingual body and tongue tip; fungiform papillae were scattered among the filiform papillae on the lingual body and tongue tip; and there were three vallate papillae at the root of the tongue. We found two strands of papillary projections in the tongue root. Despite the low variability observed in the lingual papillae, the morphological data obtained in this study may be related to the opossum's diverse food habits and the extensive geographic distribution of the species throughout America. Microsc. Res. Tech. 2012. © 2012 Wiley Periodicals, Inc.     

复合型裂纹小范围屈服下裂尖塑性区统一解

采用俞茂宏统一强度理论,推导Ⅰ、Ⅱ复合型裂纹在小范围屈服条件下裂尖塑性区尺寸的统一解析解.给出材料参数在不同拉压比α、泊松比v和中间主应力影响参数b下的一族裂尖塑性区形状与大小的轨迹.讨论以上参数对裂尖塑性区变化的影响,其中拉压比α对塑性区影响较大,α≠1导致塑性区在裂纹上下表面处不连续,b=0和b=1分别对应裂尖塑性区的上限、下限边界.同Tresca准则、Mises准则的解进行比较分析,已有解均是它的特例或线性逼近,该理论解具有理论的统一性和对不同材料的普适性.     

Measuring probe alignment errors on cylindrical coordinate measuring machines

This note describes a method for measuring probe alignment errors on precision cylindrical coordinate measuring machines. Specifically, this method is used to determine the minimum distance between the line of travel of the center of a spherical probe tip and the axis of rotation of a rotary axis. Within the Timken facility, we refer to this error as intersection error [Bryan JB. Private communication; 7 June 1992]. In addition to intersection error, this method determines the position along the probe line of travel at which the center of the probe tip passes nearest to the axis of rotation. This position is commonly referred to as probe offset error. It is used to adjust the probe location such that its radial position is zero where it intersects (or nearly intersects) the axis of rotation. In this way, the probe tip location is datumed to the axis of rotation.     

A surface flow line model of a scratching tip: apparent and true local friction coefficients

The apparent friction coefficient is the ratio between the tangential force and the normal load applied to a moving scratching tip. It includes a so-called “true local” friction coefficient, which is the scission at the interface between the tip and the surface being scratched, and a “geometrical” friction coefficient, which is the plough effect due to the wave front created ahead of the moving tip and depends on the shape of the tip. Like in any mechanical test, three basic types of behaviour of the material at the interface are observed: purely elastic, elastic–plastic and fully plastic. As is usual in polymers, the material behaviour is time and temperature dependent and may exhibit strain hardening. A surface flow line model is developed here to deduce the geometrical and true friction coefficients at the interface between a moving scratching tip and a surface from the apparent friction coefficient. Using this model, several situations may be simulated to predict the influence of the geometry of the tip on the scratch resistance of the material.     

三轴应力状态下复合型裂纹尖端前缘的塑性区分布

利用Ｍｉｓｅｓ屈服准则从理论上分析了Ⅰ－Ⅱ复合型裂纹尖端前缘的塑性区分布。推导出了由三轴应力约束参数Ｔｚ参与表征的裂纹尖端前缘塑性区尺寸ｒｐ的表达式，并绘制出了Ⅰ－Ⅱ复合型裂纹在单轴、双轴载荷作用下裂纹尖端塑性区的分布图。     

Computer simulations of the dynamic behavior of three point bend specimens

Computer simulations of the mechanical behavior of a three point bend specimen with a quarter notch under impact load are performed. Two cases with different load application points at the side and at the middle of the specimen are considered. An elastic-plastic von Mises material model is chosen. Three phases such as impact, bouncing and bending phases are found to be identified during the period from the moment of impact to the estimated time for crack initiation. The quasi static case is compared with the above two cases. It is clearly shown that no plastic deformation near the crack tip is appeared at the impact phase. However, it is confirmed that the plastic zone near the crack tip emerges in the second phase and the plastic hinge has been formed in the third phase i.e., at the end of which a quasi static state is reached.     

四级低速轴流压气机端壁区流动的实验研究

在四级低速大尺度轴流压气机试验台上,利用自行设计加工的十孔梳状附面层探针、四孔探针以及埋入高频响Kulite传感器的动态探针,针对端壁区流动展开了详细的流场测量。从附面层探针测量结果中能清晰识别出附面层区和主流区;获得了该压气机进口的附面层位移厚度、动量损失厚度、能量损失厚度及堵塞系数,且实验结果表明,采用平板紊流附面层公式能较好地进行附面层厚度的估算;采用位移机构带动四孔探针测得的第三级压气机转子进出口流场速度结果显示,受轮毂旋转作用,转子后的下端壁区附面层厚度明显要小于上端壁区附面层厚度;动态探针测量结果能较为明显地识别出叶尖泄漏涡的发展轨迹,且随着流量系数的减小,叶片尖部最大负荷点从尾缘向前缘移动,导致叶尖泄漏涡起始点前移。     

用弹塑性有限元法对焊接接头裂尖场J积分的研究

采用平面应力弹塑性有限元法研究了中心裂纹板焊接接头裂尖场J积分参量及其应用的可行性，数值分析采用MARC软件的二维弹塑性分析模型，探讨了不同强度匹配（高，等，低匹配）的焊接接头试样在加载过程中裂尖场J积分的变化情况，计算结果表明，靠近焊接接头裂纹尖端的J积分回路明显的路径相关性，而远离裂尖的J积分回路表现出路径无关性，焊接接头强度匹配因子M对裂纹尖端的J积分值有很大的影响，对应于每一个载荷P／P0，J积分的值随M的增大而减小，特别是当P／P0＞1．0时这种情况更明显。     

Dynamic plastic behavior of a free–free beam striking the mid-span of a clamped beam with shear and membrane effects considered

Recently Yu et al. (Int. J. Solids Struct. 38 (2001) 261) made a study on the dynamic behavior of a flying free–free beam striking the tip of a cantilever beam using the rigid, perfectly plastic (r-p-p) material model. Later, also based on the r-p-p material model Yang and Yu (Mech. Struct. Mach. 29 (2001) 391) analyzed another impact problem of a free rotating hinge beam striking a cantilever beam. Both of these studies ignored the finite deflection effects on the plastic behavior of the colliding beams. However if the free–free beam strikes a clamped beam, the influence of finite-deflections, or, geometric changes, must be retained in the governing equation if the maximum permanent transverse displacement of the clamped beam exceeds the corresponding beam thickness. The problem becomes more interesting since the deformation mechanisms of the beam system and the partitioning of energy dissipation in the beams are significantly different from those predicted by ignoring the influence of membrane forces. Accordingly the failure modes of the structure are different.In the present paper, a theoretical model based on the r-p-p material idealization is proposed to simulate the dynamic behavior when the mid-point of a translating free–free beam impinging on the mid-span of a clamped beam with the beam axes perpendicular to each other. The plastic behavior of the beam system is explored with shear sliding and finite deflection effects taken into account. The final deflection, the dissipation of energy within the two beams after impact and the influence of the structural and material parameters are discussed. It is shown that membrane force plays an important role during the response process, especially when the deflection is of the same order as the thickness of the clamped beam.