Cylindrical cavity expansion and contraction in pressure sensitive geomaterials

Summary A broad class of plane-strain axially-symmetric deformation patterns in geomaterials is studied within the framework of large strain pressure-sensitive plasticity. Invariant, non-associated deformationtype theories are formulated for the Mohr-Coulomb (M-C) and Drucker-Prager (D-P) solids with arbitrary hardening and accounting for an initial hydrostatic state of stress. With the M-C model we arrive at a single first order differential equation, while for the D-P solid an algebraic constraint supplements the governing differential equation. The analysis centers on the effective stress as the independent variable. A simplified treatment is given for the cavitation limit and some useful relations are derived for thin walled cylinders. The theory is applied to the triaxial calibration test for Castlegate sandstone and then used to simulate the hole closure problem. Numerical examples are provided for the case of a cavity embedded in an infinite medium subjected to external or internal pressure. Results for the D-P inner cone model were found to be in close agreement with those obtained from the M-C model.     

Deep penetration analysis with dynamic cylindrical cavitation fields

Dynamic cylindrical cavitation fields are studied for a family of plastic orthotropic solids with arbitrary strain hardening response. Analysis is within the framework of plane-strain, steady state flow theory of associated plasticity. New formulae for cavitation pressure are validated against accurate numerical analysis and contact is made with existing studies. A uniform procedure is presented for estimating penetration depth of rigid axisymmetric projectiles at normal impact. Comparison with available experimental data reveals a very good agreement for both spherical and cylindrical dynamic cavitation models. Quasi-static cavitation pressure formulae can predict penetration depth with an appropriate scaling of the yield stress. The scaling factors appear to be independent of material properties but reflect the shape of head profile.     

一种测定空化水喷丸工艺中冲击压力场分布规律的方法

空化水喷丸是用于金属材料表面改性的一项新技术,它依靠自身的技术特点和优势,在金属表面改性技术领域中引起许多学者的广泛关注。该工艺中的空化行为涉及高速、高压、多相、相变、湍流、非定常特性等复杂多变情况,对该工艺中的冲击压力场分布规律的求解和测量一直是该领域的难题。本研究使用FUJIFILM压敏纸对空化水喷丸工艺中冲击压力场的分布规律进行实验测定,同时利用X射线衍射仪对该工艺诱导残余应力分布规律进行了实验测定,结果表明利用压敏纸测定空化水喷丸工艺中冲击压力场分布规律的可靠性,同时也表明该工艺可以诱导金属材料的表层形成残余压应力。     

高压喷嘴空化初生的大涡模拟

考虑瞬时压力脉动对空化初生的影响,采用动态亚格子应力模型对某高压柴油喷嘴内部瞬时流动进行大涡模拟。计算结果表明:喷孔入口分离形成的局部低压区内时均湍流脉动压力可达时均静压的2倍,两相流场时均空泡位置及形态与实验结果十分吻合,并与基于时均静压及湍流脉动压力预测的空化初生区域基本一致。分离剪切层失稳形成柱状涡并激发了转捩过程,在分离转捩区域柱状涡发生扭曲变形并产生强烈的瞬时压力脉动,从而导致了空化。喷孔入口倒角处理使得分离减弱,对分离转捩过程和空化初生具有抑制作用。     

Dynamic cylindrical cavity expansion in an incompressible elastoplastic medium

Summary Self-similar dynamic expansion of a pressurized circular cylindrical cavity, embedded in an infinite elastoplastic incompressible medium, is here investigated with the large strain J₂ flow theory. Assuming steady-state conditions, thus bypassing the initial loading history, it is shown that plane-strain fields are sustained with no diverging logarithmic stress appearing in the remote elastic field. Yet, even in the absence of remotely applied stress, the appearance of small stresses at infinity is unavoidable. The present solution is exact but limited to relatively low cavity expansion velocities. A closed form expression is given for the cavitation pressure with elastic/perfectly-plastic response. A fairly general result is derived for the cavitation pressure in hardening media with a definite yield point and in linear-hardening solids as a special case. Contact is made with earlier results of quasi-static cavity expansion along with a comparison to the self-similar dynamic expansion of a spherical cavity in an incompressible Mises solid. Upper and lower bounds for penetration depth tests are suggested by using the present cylindrical cavitation model and the incompressible spherical cavitation model.     

Cavitation Instabilities in Plastics and Rubber-Modified Plastics

Spherical void expansion in plastics and rubber-modified plastics is investigated under radial traction conditions. The plastics are modeled as elastic-plastic pressure-sensitive materials and the rubbers are modeled as nonlinearly elastic materials. First, the growth of a spherical void in an infinite plastic matrix is investigated under remote radial traction conditions. The results show that the cavitation stress of the plastic decreases significantly as the pressure sensitivity increases. Then, the growth of a spherical void located at the center of a spherical rubber particle in an infinite plastic matrix is investigated under remote radial traction conditions. The results indicate that without any failure criteria for the rubber, the cavitation stress does not exist when the void is small and the rubber is characterized by high-order strain energy functions. However, when a failure criterion for the rubber is considered at a finite stretch ratio, the results show that the cavitation stress for the plastic with the rubber particle becomes close to that for the plastic without the rubber particle. This revised version was published online in August 2006 with corrections to the Cover Date.     

Assessment of notched tubular ferritic oxide-dispersion-strengthened components subjected to multiaxial creep loading at 1100°C

Notched tubular components of a ferritic oxide-dispersion-strengthened material, MA 956, were subjected to multiaxial creep loading at 1100°C by applying a constant internal pressure. The components proved to be extremely insensitive to circumferential notches of up to 80 percent of the wall thickness due to the high axial creep rupture strength of this material. However, the components were sensitive to both externally and internally axially aligned notches, and displayed similar stress rupture behaviour but consistently longer rupture lives than plane components at the same ligament stress level. Failure was found to be due to strain controlled cavitation in the ligament rather than as a consequence of creep crack growth from the notch. A direct current/potential drop method was shown to provide a reasonable indication of the development of cavitation in these tests. It is shown that the low ductility failure of notched MA 956 components is best described by a creep fracture mechanism rather than by fracture mechanics.     

CREEP LIFE OF AISI 316 STAINLESS STEEL SUBJECTED AT 550°C TO STEP CHANGES IN TENSILE LOAD

Abstract— A phenomenological model of cumulative creep damage combining simulated grain boundary cavitation with internal redistribution of stress is developed and matched to constant load tensile creep data for an AISI 316 stainless steel tested at 550°C. The model is shown to predict the creep life of the material when it is subjected to single step changes in load provided the strain rates subsequent to the change are imposed in the model. It is inferred that this supports current suggestions that cavitation failure may be strain controlled.     

高压喷嘴内部空化流动的数值模拟研究

高压柴油喷嘴入口流动分离产生的局部低压会诱发空化现象。该文利用k-ω SST 两方程湍流模型和k-kl-ω湍流/转捩模型对某喷嘴内无空化及空化流动进行数值模拟。结果表明k-kl-ω模型可有效预测喷嘴入口回流区分离转捩过程, 且喷孔内空化流的空泡位置、形态及出口质量流量与实验结果吻合很好, 能更准确模拟喷嘴内空化流动, 而k-ω SST 模型忽略了分离转捩过程, 难以预测喷嘴内部的初生空化及流动特性。进而采用k-kl-ω模型探讨了喷嘴入口回流区流动结构及转捩过程对空化初生及发展的影响, 揭示出回流区长度、压力及脉动能强度分布特性, 为深入研究喷嘴射流雾化机理提供依据。     

伴随气泡和气穴的低压液压管路瞬态分析

利用流体动力学原理,基于低压液压管路瞬态脉动过程中气泡和气穴同时存在的假设,在连续方程和运动方程的基础上,建立了低压液压管路中伴随气泡和气穴的瞬态脉动数学模型,给出了摩擦阻力项数学模型以及气泡和气穴的体积计算数学模型。并采用有限差分法和Matlab/Simulink,对一段等径水平直管道中有气泡和气穴产生时的压力瞬态脉动特性进行了仿真分析和实验研究。瞬态压力脉动波的仿真结果与实验数据的比较表明:所提出的伴随气泡和气穴的低压液压管路瞬态数学模型是合理的,仿真方法是可行的。     

扰动情况下双油槽圆形轴瓦滑动轴承性能分析

采用FLUENT软件及其提供的气穴模型,计算了双油槽圆形轴瓦滑动轴承的油膜压力分布及气穴存在区域大小和位置,并同其他边界条件进行了对比;讨论了进油压力对轴承的流场和承载能力的影响;利用自行改进的动网格技术对轴颈扰动速度对流场和油膜力的影响进行了非稳态计算。计算结果表明,进油压力对油膜力的影响较大,油膜压力受轴颈扰动速度的影响很大,油膜力与轴颈扰动速度明显呈非线性关系,利用改进的动网格技术可以很好地对轴承的动特性进行分析。论文为今后大扰动条件下转子-轴承系统的非线性动特性分析打下了基础,为滑动轴承的设计提供了一种理论参考依据     

超塑性Y-TZP的高温塑性流动行为

通过恒位移速度压缩试验研究了不同晶粒大小,不同致密度的３Ｙ－ＴＺＰ的高温塑性流动行为。结果表明,塑性流动应力随着温度和应变速率的提高及晶粒尺寸的增大而提高,随着气孔率的增大而下降,对于晶粒较粗的试样,当应力水平较高时,由于材料内部产生孔穴化,引起屈服后流动应力下降。细晶３Ｙ－ＴＺＰ在高温塑性形变过程中产生应变硬化,这是由于形变过程中晶粒动态生长和应变速率提高而引起。     

基于FLUENT的高压高速螺旋转子泵内部流场分析

目的分析高压高速螺旋转子泵运行过程中的内部流场行为,为高压高速螺旋转子泵的结构优化提供理论依据。方法利用Solid Works建立高压高速螺旋转子泵三维模型,使用FLUENT仿真其在高压高速运行条件下的内部流场,得到压强云图,对比有、无气穴时转速对油膜最大压强和最大负压影响。结果气穴对高压区的啮合压强基本没有影响。齿轮啮合处压强最大值、齿轮啮合处负压最大值及空气在液压油中的占有率随转速的增加而增大,当转速为12 000 r/min时,空气占有率高达12.81%,啮合处的压强可高达37.5 MPa,是出油口压强的1.5倍。结论气穴阻止了部分齿顶间隙的泄漏,对转子稳定性的提高有积极意义。最大压强出现在螺旋转子泵转子的啮合处,这使转子产生了剧烈振动,降低了螺旋转子泵的稳定性。     

Quantification of pressure-induced hoop stress effect on fracture analysis of circumferential through-wall cracked pipes

This paper provides engineering J and crack opening displacement (COD) estimation equations for through-wall cracked (TWC) pipes under internal pressure and under combined internal pressure and bending. Based on selected 3-D FE calculations for the TWC pipe under internal pressure using power law materials, elastic and plastic influence functions for fully plastic J and COD solutions are tabulated as a function of the normalised crack length and the mean radius-to-thickness ratio. These developed GE/EPRI-type solutions are then re-formulated based on the reference stress concept. Such re-formulation not only provides simpler equations for J and COD estimation, but also can be easily extended to combined internal pressure and bending. The proposed reference stress based J and COD estimation equations are compared with elastic-plastic 3-D FE results using actual stress-strain data for Type 316 stainless steels. The FE results for both internal pressure cases and combined internal pressure and bending cases compare very well with the proposed J and COD estimates.     

Fundamental solutions of cavitation in porous solids: a comparative study

The expansion of internally pressurized cavities, embedded in infinite bodies, in spherical and cylindrical (plane strain and plane stress) configurations, is investigated within the framework of finite plasticity. Material response is modeled by the Gurson theory for porous solids and includes strain hardening. Numerical results, obtained under the assumption of nearly universal loading histories, reveal limit cavitation states for all three deformation patterns. Cavitation is identified with asymptotic levels of the specific cavitation energy, which is highest for the spherical cavity and smallest for plane stress (plate) holes. The influence of material porosity is assessed in context of weight optimization of protective plates. A limited comparison with experimental data for porous titanium plate perforation reveals close prediction of ballistic limit velocity.     

Nucleation of Bubbles by Electrons in Liquid Helium-4

We report on experiments in which we study cavitation resulting from electrons in liquid helium. Electrons are introduced into the liquid by a radioactive source. After an electron comes to rest in the liquid, it forces open a small cavity referred to as an electron bubble. To study cavitation, a sound pulse is generated by means of a hemispherical piezoelectric transducer producing a large-amplitude pressure oscillation at the acoustic focus. If an electron is in the vicinity of the focus and the negative-going pressure swing exceeds a critical value, a cavitation bubble is produced which can be detected by light scattering. Two distinct critical pressures \( P_{\text{el}} \) and \( P_{\text{rare}} \) have been measured. The first corresponds to cavitation resulting from the application of a reduced pressure to liquid containing an electron which has already formed an electron bubble. The second is the critical pressure needed to lead to cavitation when an electron enters the liquid at a time and place where there is already a reduced pressure. We have measured these two pressures as a function of temperature and consider possible explanations for the difference between them. In addition to these clearly seen cavitation thresholds, there are some cavitation events that have been detected with a threshold that is at an even smaller negative pressure than \( P_{\text{el}} \) and \( P_{\text{rare}} \).     

Fatigue analysis of damaged steel pipelines under cyclic internal pressure

A methodology for fatigue analysis of damaged steel pipelines under cyclic internal pressure is proposed. This methodology employs stress concentration factors, which are commonly used to modify standard S–N curves of metallic structures under high cycle fatigue loadings. Experiments are accomplished to evaluate the strain behavior of small-scale steel pipes during denting and cyclic internal pressure. A nonlinear finite element model is developed to obtain stress concentration factors induced by plain dents on steel pipes under internal pressure. Afterwards, analytical expressions are developed to estimate stress concentration factors as function of the damaged pipe geometric parameters. Finally, fatigue tests are conducted to evaluate the finite life behavior of small-scale damaged pipes under cyclic internal pressure and to validate the proposed methodology of fatigue analysis.     

The sonically induced cavitation of liquid helium

The onset of sonically induced cavitation in liquid helium at frequencies between 30 and 40 kHz has been studied. In helium II, two types of cavitation activity were identified: acoustic cavitation whose characteristic noise can be detected, and visible cavitation in which vaporous cavities grow to visible size. The onset of acoustic cavitation is statistical in nature with increasing event rates as the sound pressure amplitude is increased and whose threshold depends on the waiting time at that particular amplitude. The acoustic threshold sound pressure amplitude in helium II between 1.8° K andT was found to lie within 0.15 mb of 0.3 mb, the variation of ±0.15 mb occurring from one determination to another, whereas the sound pressure amplitude corresponding to the visible threshold was about a hundred times larger. These two distinct types of sonically induced cavitation appear to be unique to liquid helium. However, aboveT the two thresholds were found to coincide at a sound pressure amplitude within 0.4 mb of 0.8 mb. The characteristics of the onset of acoustic cavitation were found to be independent of applied static pressure of up to 1.5 atm above and belowT and in helium II they were unaffected by filtering, heat flushing, or rotating the liquid. The results suggest that liquid helium is nucleated by random events initiated by the ambient cosmic radiation or by vortices generated in the liquid, and they imply that at ultrasonic frequencies this liquid cannot withstand a tensile stress and behaves in this respect like water saturated with gas and containing dust motes. Attempts to determine the onset of acoustic cavitation by scattering light off the bubbles or by detecting sonoluminescence were not successful: The upper limit to the size of these bubbles was shown to be about 30 µm and the intensity of any sonoluminescence must have been less than 10^–4 of that from cavitating water. The possibilities of exploiting the two types of cavitation activity in liquid helium in the construction of a posttriggerable ultrasonic bubble chamber for visualizing the tracks of ionizing particles are discussed, as are the theoretical background and future development of the work presented in this paper.     

Nylon-6-rubber blends

The macroscopic cavitation and yield behaviour of nylon-6/rubber blends was studied. The type of rubber (poly(butadiene), ethylene propylene copolymer (EPDM) or polyethylene (LDPE), the rubber concentration and the rubber particle size was varied. The onset of cavitation was determined by measuring the intensity of the transmitted light from an incident laser beam. Both the yield stress and the cavitation stress appeared to increase with increasing strain rate and rubber modulus. No linear relation between the shear modulus and the cavitation stress was found. The data indicate that blends with a very small particle size have a relatively high cavitation stress. In all cases, a high cavitation stress of the elastomer resulted in a high yield stress of the blend.