Transient dynamic fracture analysis by an extended meshfree method with different crack-tip enrichments

Investigation of transient dynamic stress intensity factors (DSIFs) of two-dimensional fracture problems of isotropic solids and orthotropic composites by an extended meshfree method is described. We adopt the recently developed extended meshfree radial point interpolation method (X-RPIM), which combines either the standard branch functions or the new linear ramp function associated with Heaviside functions to capture crack-tip behaviors. It is the first time the linear ramp function integrating into meshfree X-RPIM has been presented in a dynamical fracture context. We are particularly interested in exploring insight into the behaviors of DSIFs under dynamic impact loadings (e.g., step, blast and sine loading types) using our meshfree method. For some of these problems numerical examples have been performed using the new ramp functions, and the obtained results of DSIFs have also been compared with those using the standard enrichment functions under which the two schemes have the same setting. In each case it is found that the numerical solutions delivered using the X-RPIM associated with the ramp enrichments are in good agreement with those with the standard functions. The paper first describes formulations and then provides verification of our developed approach through a series of numerical examples in transient dynamic fracture for both solids and orthotropic composites. Illustration of scattered elastic stress waves propagating in the cracked body is depicted to take an insight look at the behavior of dynamic response.     

螺旋压缩弹簧应力松弛特性试验分析及其应用

本文通过应力松弛试验、理论推导及数值模拟研究了高温下螺旋压缩弹簧的应力松弛规律,并利用加速模型对工况下弹簧应力松弛服役寿命做出预测。首先,根据螺旋压缩弹簧的结构特点搭建了弹簧应力松弛连续动态测试装置,该装置不仅避免了传统测试方法存在的缺陷,而且能够保证试验过程中位移载荷恒定,并实时监测载荷变化。本文以某飞机舱门单锁机构中的螺旋压缩弹簧为试验对象进行了不同温度条件下的应力松弛试验,得到其松弛动力学曲线,并基于Arrhenius模型建立了弹簧在工况下的应力松弛服役寿命预测模型;其次,基于应力松弛和蠕变在本质上的一致性,结合金属材料蠕变规律并根据试验弹簧的受力特点,推导出用于描述试验材料松弛行为的蠕变本构方程,由试验结果获得该本构方程的材料常数;最后,通过该本构方程及材料常数,在ANSYS软件中对试验弹簧的松弛过程进行模拟,结果表明,模拟结果与试验结果误差不大于4%。因此,通过本文方法所建立的蠕变方程对弹簧在不同载荷条件下的应力松弛规律进行仿真分析具有一定的可行性与准确性。     

U–6Nb shear stress relaxation in compression waves (IJP 585-AV)

When uranium alloyed with 6-wt% niobium (U–6Nb) is rapidly compressed in uniaxial strain experiments, shear stress is observed to relax with a characteristic time of 30 ± 7 ns. In shock wave experiments, this relaxation inhibits the development of an elastic precursor commonly seen in other materials. When U–6Nb is cold-rolled to pre-twin and significantly increase the density of dislocations in the material, stress relaxation effects are diminished suggesting that twinning causes relaxation in the un-worked material. Separate ramp wave compression experiments produce effects that agree with those observed in shock-loading experiments. A phenomenological model is introduced that allows accurate simulation of all experiments. Estimates of residual shear stress after relaxation are obtained.     

竖向均布荷载作用在地基内部时的土中应力公式

建筑物基础一般都是埋入地基中，且有一定深度，而目前土中应力计算所常依据的布西奈斯克解却是假定荷载地表面导出的。本文以半无限体内受竖向力作用的明德林公式为根据，通过积分而首次完整地推导出竖向矩形均布荷载作用在地基内部上的土中应力分量解析表达式，并与布氏公式进行比较，说明其应用范围，以便于工程设计人员在设计时使用。     

Path dependence and multiaxial behavior of a polycrystalline NiTi alloy within the pseudoelastic and pseudoplastic temperature regimes

Several multiaxial experiments on polycrystalline NiTi have been conducted within a wide temperature range. In this vein, the pseudoelastic as well as the pseudoplastic behavior are investigated within the distinct temperature regimes. Isothermal and temperature varying thermomechanical loading paths are applied by means of an active temperature control in order to characterize the path dependence of pseudoelasticity and the multiaxial one-way effect of the alloy. The main focus is on the determination of the dependence of the loading sequence, the related non-linearity of the material and the combined material interaction, e.g., referring to reorientation processes for complex loading paths with respect to pseudoelasticity and the one-way effect. Isothermal tension/compression/torsion experiments are performed on an austenitic microstructure spanning all four quadrants of the axial/torsional strain subspace. In this regard, it is deduced in the course of this contribution that the apparently qualitatively different material behavior for different strain paths in the pseudoelastic temperature regime might be explained by the axial/torsional and tension/compression asymmetry. Furthermore, some multidimensional axial/torsional stress controlled experiments are realized with loading on a martensitic and unloading being implemented both on martensitic and austenitic microstructures. Here, the peculiarity of the one-way effect referring to apparently different transformation temperatures is ascribed to the loading history of the specimen material and to differently oriented martensite variants. In order to elucidate these effects, potential explanations for the pseudoelastic path dependence and the non-linearity in the material behavior with reference to the multiaxial one-way effect are presented.     

Boltzmann superposition principle for a time-dependent soft material: assessment under creep flow field

Variety of time-dependent soft materials that undergo evolution of microstructure are known to follow the Boltzmann superposition principle when appropriately transformed from the real to the effective time domain. This behavior is attributed to obliteration of time dependency in the effective time domain by normalizing the real time by the time-dependent relaxation time. This work is aimed at assessing validity of the Boltzmann superposition principle in the effective time domain under application of step changes and ramps in stress for a time-dependent soft glassy material: an aqueous suspension of Laponite, whose rheological properties are known to show strong time and stress dependency. Interestingly, creep experiments started at different aging times and for different constant stresses indeed lead to a comprehensive time–aging time–stress superposition resulting in time and stress dependence of relaxation time and modulus. Subsequently, we analyze compliance response of the material to different kinds of stress step change and ramp combinations. We observe that except few, most of the compliance data plotted in the effective time domain does not overlap on the comprehensive superposition. We analyze this behavior and attribute the observed mismatch to the history dependence of the time evolution of modulus.     

层合材料的非傅里叶热传导及热应力

论文建立了一个双层材料层合板受瞬态加热情况下的非傅里叶热传导分析模型,用向后差分法得到了温度场的数值解,并对该差分格式的稳定性进行了讨论.给出了温度场随导热时间、热扩散率、空间与时间步长之比以及弛豫时间的变化趋势.同时,通过已经求得的温度场,求得了层合板内的应力场,给出了层合板内的热应力随时间的变化.     

SHPB试验中粘弹性材料的应力均匀性分析

采用特征线解法，对满足ZWT方程的粘弹性材料在高应变率SHPB试验中的应力均匀性进行了数值研究。着重分析了不同的材料本构粘性(松弛时间)、瞬态波阻抗比和入射波升时对于试样中应力均匀性、应变均匀性和平均应变率等的影响。为今后动态试验的试样设计提供了一定的理论依据。     

静压沉桩挤土机理探讨及有限元分析

针对预制桩在静压沉桩过程中出现的挤土现象,从土体小主应力方向加载的角度考虑,视浅层土体的隆起为小主应力方向(水平向)加载引起大主应力(垂直向应力)增加所致.在已有的柱形小孔扩张理论基础上,通过引入考虑位移的土压力计算方法提出了桩周土体隆起分界面表达式.利用该表达式分析浅层土体的隆起量,并利用Randolph提出的深层土体径向位移解析公式给出深层土体的变形量.最后运用有限元数值模拟计算与本文的数值解答进行对比分析,结果相近.     

粘弹性地基上粘弹性输流管道的稳定性分析

从Winkler假设和单轴线性粘弹性本构方程出发,推导了Kelvin-Voigt粘弹性地基上三参量固体模型输流管道的运动微分方程,采用改进的有限差分法,分析了管道和地基的粘弹性参数对输流管道无量纲复频率和无量纲流速之间的变化关系的影响。     

岩石三轴蠕变试验黏弹性解析及参数识别

基于岩石三轴蠕变试验,推导了相应的黏弹性解析解,并对三参量H-K流变模型给出 了黏弹性解析解的显式以及流变参数的识别方法. 在此基础上,针对花岗岩及片岩两种岩石 的室内蠕变分级加载试验曲线进行了流变参数的识别与反演. 分析表明,同一岩样在不同加 载级别下的弹性及黏弹性参数在量值上均有所不同,其中黏弹性模量和黏滞系数的量值随 载荷的增加出现损伤衰减,基于试验反演所获参数的解析蠕变曲线与试验蠕变曲线吻合较好.     

基于应变能的复杂应力场低周疲劳分析

塑性应变能使材料微观组织结构发生不可逆变化,从而引起等效宏观应力,该应力随循环加载而增大．假定材料疲劳源处破坏是由最大拉应力引起的,最大等效宏观应力与外加应力叠加达到材料本征断裂应力时形成微裂纹．微裂纹引起上述两部分应力变化,继续加载直至宏观裂纹出现,从而得到材料的疲劳寿命．本文所建立的多轴疲劳寿命公式包含材料参数、拉应力以及塑性应变能等,以上数据可通过单轴疲劳数据和有限元方法获得．通过对SM45C材料的计算验证,表明该模型对多轴随机应变加载低周疲劳寿命,具有良好的预测结果．     

An analytical solution and analysis of characters for viscoelastic fluid flow in annular pipe

I.Introducti0nLuiCiqunandHuangJunqiI'I(l989),ZhuWeihuiandLuiCiquri1'l(l992)sequentiallystudiedtheaxialflowofsecondorderandMaxwellfluidsandanalyzedtheflowcharactersofthesefluids.Thispaperwillstudyunsteadyrotat0ryflowofsecondorderandMaxwellfluidsinannularpi…     

PREDICTION OF THE VISCOELASTIC PROPERTIES OF THE EQUIVALENT PARTICLE FOR THE INTERCALATED MULTI-LAYER STACK OF NANOPLASTICS

The aim of this paper is to apply the asymptotic homogenization method to deter- mining analytically and numerically the transversely isotropic viscoelastic relaxation moduli of the equivalent particle for the intercalated multi-layer stack of intercalated type nanoplastics.A two-phase multilayered material containing n layers is considered.The matrix is assumed to be an isotropic viscoelastic standard linear body and the reinforcement is assumed to be an isotropic elastic body.Final explicit analytical formulae for the effective elastic moduli of the multilay- ered material are derived first;and then the correspondence principle is employed to obtain the homogenized relaxation moduli of the equivalent intercalated particle.A numerical example is given.Final explicit analytical formulae in the time domain derived here make it convenient to estimate the influence of all the particle parameters of micro-structural details on the effective properties of the equivalent intercalated particle.The results of this paper can also be applied to multi-layer composites.     

混凝土桥梁拼接后收缩徐变计算方法分析

为分析混凝土收缩徐变对新旧拼接混凝土桥梁的影响,考虑每个计算步长内由混凝土收缩引起的应力的徐变作用和混凝土的弹性模量变化,根据能量原理推导了混凝土收缩徐变的位移法基本方程。分别按每个计算步长内应力为变值和常值,采用增量法推导了每个计算步长内收缩徐变的递推计算公式,并编制了相应的计算程序。对比分析表明,按每个计算步长内应力为变值的计算结果与实测值吻合良好,与每个计算步长内应力为常值相比,可以增大计算步长,减少叠加次数,大大加快程序计算速度。     

Experimental identification and mathematical modeling of viscoplastic material behavior

Uniaxial torsion and biaxial torsion-tension experiments on thin-walled tubes were carried out to investigate the viscoplastic behavior of stainless steel XCrNi18.9. A series of monotonic tests under strain and stress control shows nonlinear rate dependence and suggests the existence of equilibrium states, which are asymptotically approached during relaxation and creep processes. Strain controlled cyclic experiments display various hardening and softening phenomena that depend on strain amplitude and mean strain. All experiments indicate that the equilibrium states within the material depend on the history of the input process, whereas the history-dependence of the relaxation and creep behavior appears less significant. From the experiments the design of a constitutive model of viscoplasticity is motivated: The basic assumption is a decomposition of the total stress into an equilibrium stress and a non-equilibrium overstress: At constant strain, the overstress relaxes to zero, where the relaxation time depends on the overstress in order to account for the nonlinear rate-dependence. The equilibrium stress is assumed to be a rate independent functional of the total strain history. Classical plasticity is utilized with a kinematic hardening rule of the Armstrong-Frederick type. In order to incorporate the amplitude-dependent hardening and softening behavior, a generalized arc length representation is applied [14]. The introduction of an additional kinematic hardening variable facilitates consideration of additional hardening effects resulting from the non-radiality of the input process. Apart from the common yield and loading criterion of classical plasticity, the proposed constitutive model does not contain any further distinction of different cases.The experimental data are sufficient to identify the material parameters of the constitutive model. The results of the identification procedure demonstrate the ability of the model to represent the observed phenomena with satisfactory approximation.     

随机应力过程下半椭圆型表面裂纹的扩展

本文应用随机平均原理研究了在随机载荷作用下具有随机抗裂特性的构件所含半椭圆型表面裂纹的疲劳扩展。导出了支配半椭圆型表面裂纹尺寸的转移概率密度的ＦＰＫ方程，给出了裂纹扩展方程在表面和深度两个方向互不耦合情形下的解析解。通过数例详细考察了具有确定性抗裂特性的构件所含半椭圆型表面疲劳裂纹在平稳窄带高斯应力作用下的扩展行为，并有和数字模拟验证方法的有效性。     

Experimental determination of the relaxation modulus of a linear-isotropic-viscoelastic material

It is well known that the relaxation modulus of a linear-isotropic-viscoelastic material under uniaxial load is the stress history of a unit-step strain history. A unit-stepped strain function cannot be obtained with the common instron testing machine. Instead, an easily obtainable strain function is described from which the relaxation modulus is derived. Experiments were conducted to illustrate this method. Experimental-data-reduction techniques are described. Experimentally measured output stress vs. time is fitted by a ‘smooth’ polynomial using a least-square criterion. Then by differentiation of this polynomial at proper times, the relaxation function is obtained.     

Thickness dependence of viscoelastic stress relaxation of laminated microbeams due to mismatch strain

Time-dependent behaviors due to various mismatch strains are very important to the reliability of micro-/nano-devices. This paper aims at presenting an analytical model to study the viscoelastic stress relaxation of the laminated microbeam caused by mismatch strain. Firstly, Zhang’s two-variable method is used to establish a mechanical model for predicting the quasi-static stress relaxation of the laminated microbeam. Secondly, the related analytical solutions are obtained by combining the diffe...     

Prediction of the creep behaviour of polyethylene and molybdenum from stress relaxation experiments

In many applications it is useful to be able to convert observed creep data of a material to corresponding stress relaxation data or vice versa. If the material exhibits non-linear viscoelasticity such a conversion can be rather difficult. In this paper two semi-empirical flow equations, the power law and the exponential law, are used to convert stress relaxation data into corresponding creep behaviour data. These two flow equations are often used to describe non-linear viscoelastic behaviour. The procedure adopted here is based on the assumption that the creep data during the experiment decrease due to an increase in the internal stress level, thus decreasing the effective stress for flow. The conversion method is applied to high density polyethylene and polycrystalline molybdenum at room temperature. In general predictions using the power law are in better agreement with the experimental results than predictions using the exponential formula. The concepts of secondary and ceasing creep are discussed in terms of build-up of internal stress during the creep process.