THE VOID-SIZE EFFECT ON PLASTIC FLOW LOCALIZATION IN THE GURSON MODEL

Recent studies have shown that the size of microvoids has a significant effect on the void growth rate.The purpose of this paper is to explore whether the void size effect can influence the plastic flow localization in ductile materials.We have used the extended Gurson's dilatational plasticity theory,which accounts for the void size effect,to study the plastic flow localization in porous solids with long cylindrical voids.The localization model of Rice is adopted,in which the material inside the band may display a different response from that outside the band at the incipient plastic flow localization.The present study shows that it has little effect on the shear band angle.

Extension of the gurson model accounting for the void size effect

A continuum model of solids with cylindrical microvoids is proposed based on the Taylor dislocation model. The model is an extension of Gurson model in the sense that the void size effect is accounted for. Beside the void volume fraction f, the intrinsic material length l becomes a parameter representing voids since the void size comes into play in the Gurson model. Approximate yield functions in analytic forms are suggested for both solids with cylindrical microvoids and with spherical microvoids. The application to uniaxial tension curves shows a precise agreement between the approximate analytic yield function and the exact parametric form of integrals.

Micro-plasticity Constitutive Model Taking Account of Size Effects for Pure Aluminum by Microindentation

The macro-plasticity power function constitutive model （MPFCM）, the modified macro- plasticity power function constitutive model （MMPFCM） and the micro-plasticity constitutive model （MCM） taking the material intrinsic length were established to characterize the microindentation size effects of pure aluminum, respectively. The experimental results indicated MPFCM only determined precisely in the great indentation load. While a modified one named MMPFCM was subsequently established taking account of the parameters variation with the increase of indentation depth. The conventional dimensional analysis method was employed to determine the strength coefficient K and the strain hardening exponent n of this modified model. And then MCM taking account of size effects was proposed based on the Taylor dislocation model. The first- order steepest gradient descent method was adopted to obtain the material intrinsic length for the geometrically necessary dislocations. The parameters of MCM were identified by using the UMAT subroutine of ABAQUS software. The average absolute relative error of MCM is relatively lower than that of the macro-one. Although the precision of the modified one is also high, the applied scope is limited, only for the microindentation material. In addition, the intrinsic length 5.09 bun of pure aluminum is also obtained based on the strain gradient theory.

Simulation of size effects by a phase field model for fracture

In phase field fracture models the value of the order parameter distin- guishes between broken and undamaged material. At crack faces the order param- eter interpolates smoothly between these two states of the material, which can be regarded as phases. The crack evolution follows implicitly from the time inte- gration of an evolution equation of the order parameter, which is coupled to the mechanical field equations. Among other phenomena phase field fracture mod- els are able to reproduce crack nucleation in initially sound materials. For a 1D setting it has been shown that crack nucleation is triggered by the loss of stability of the unfractured, spatially homogeneous solution, and that the stability point depends on the size of the considered structure. This work numerically investi- gates to which extend size effects are reproduced by the 2D phase field model. Exemplarily, a finite element study of the hole size effect is performed and the simulation results are compared to exnerimental data.

Collinear micro-shear-bands model for grain-size and precipitate-size effects on the yield strength

Numerous experimental evidences show that the grain size may significantly alter the yield strength of metals.Similarly,innickel-based superalloys,the precipitate size also influences their yield strength.Then,how to describe such two kinds of size effects on the yield strength is a very practical challenge.In this study,according to experimental observations,a collinear micro-shear-bands model is proposed to explore these size effects on metal materials’yield strength.An analytical solution for the simple model is derived.It reveals that the yield strength is a function of average grain-size or precipitate-size,which is able to reasonably explain size effects on yield strength.The typical example validation shows that the new relationship is not only able to precisely describe the grain-size effect in some cases,but also able to theoretically address the unexplained Hall-Petch relationship between theprecipitate size and the yield strength of nickel-based superalloys.

Fama-French-factor model,size and book-to-market effect:An empirical investigation of the Chinese stock market

In this study, we use Chinese A-share stock market data from 1995 to 2005 to test the persistence of the size and valueeffect and the robustness of the Fama-French three-factor model in explaining the variation in stock returns.Wefind that the three-factor model can explain the common variation in stock returns well.However, it is mis-specifiedfor the Chinese stock market.We demonstrate that the size effect and the book-to-market effect are significant andpersistent over our sample period.Interestingly, the book-to-market effect for China is much stronger than the averageones in mature markets and other emerging markets documented by Fama and French (1998).Moreover, we find noevidence to support the argument that seasonal effects can explain the results of the multifactor model.Last, our mixedobservations on firm-specific fundamentals suggest that the risk-based explanation proposed by Fama and French(1995) cannot shed light on the size and BM effect for China.In view of the features of the Chinese stock market, weinstead argue that China’s size and book-to-market effect may be attributed to syndicate speculators’ manipulation andmispricing caused by irrational investor behavior.

Modeling size-dependent thermo-mechanical behaviors of shape memory polymer Bernoulli-Euler microbeam

The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer (SMP) microbeam.Size-dependent constitutive equations,which can capture the size effect of the SMP,are proposed based on the modified couple stress theory (MCST).The deformation energy expression of the SMP microbeam is obtained by employing the proposed size-dependent constitutive equation and Bernoulli-Euler beam theory.An SMP microbeam model,which includes the formulations of deflection,strain,curvature,stress and couple stress,is developed by using the principle of minimum potential energy and the separation of variables together.The sizedependent thermo-mechanical and shape memory behaviors of the SMP microbeam and the influence of the Poisson ratio are numerically investigated according to the developed SMP microbeam model.Results show that the size effects of the SMP microbeam are significant when the dimensionless height is small enough.However,they are too slight to be necessarily considered when the dimensionless height is large enough.The bending flexibility and stress level of the SMP microbeam rise with the increasing dimensionless height,while the couple stress level declines with the increasing dimensionless height.The larger the dimensionless height is,the more obvious the viscous property and shape memory effect of the SMP microbeam are.The Poisson ratio has obvious influence on the size-dependent behaviors of the SMP microbeam.The paper provides a theoretical basis and a quantitatively analyzing tool for the design and analysis of SMP micro-structures in the field of biological medicine,microelectronic devices and micro-electro-mechanical system (MEMS) self-assembling.

Numerical study of size effect in concrete penetration with LDPM

Projectile size effect is of great importance since the scaling researches are extensively applied to concrete penetration investigations. This paper numerically deals with the projectile size effect on penetration resistance via the recently developed Lattice Discrete Particles Model(LDPM) which is featured with mesoscale constitutive laws governing the interaction between adjacent particles to account for cohesive fracture, strain hardening in compression and compaction due to pore collapse. Simulations of two different penetration tests are carried to shed some light on the size effect issue. The penetration numerical model is validated by matching the projectile deceleration curve of and predicting the depth of penetration(DOP). By constant velocity penetration simulations, the target resistance is found to be dependent on the projectile size. By best fitting numerical results of constant velocity penetration, a size effect law for target resistance is proposed and validated against literature data. Moreover, the size effect is numerically obtained in the projectile with longer extended nose part meanwhile the shorter extended nose is found to improve the DOP since the projectile nose is sharpened.

Size effect on longitudinal MOE of microtomed wood sections and relevant theoretical explanation

It has been repeatedly observed that the mechanical properties of microtomed wood sections are significantly lower than those of samples of normal size, but few investigations have been conducted to deal with this topic, especially based on theoretical approaches. We measured the longitudinal MOE of Chinese fir on microtomed sections ranging in thickness from 70 to 200 μm and compared these with the values of samples of normal size. The results indicate that the MOE of microtomed wood sections increases with thickness from 70 to 200 μm, but is significantly less than that of normal samples. A size effect coefficient of 2.63 is inferred based on statistical data for samples of normal size and 200 μm thick microtomed sections. Finally, an explanation based on a complete shear restraint model of cell walls and a single fiber multi-ply model is proposed for the size effect on stiffness of microtomed wood sections.

Statistical damage constitutive model for concrete materials under uniaxial compression

According to the damage mechanism of concrete material during the uniaxial compressive failure process,this paper further establishes the statistical damage constitutive model of concrete subjected to uniaxial compressive stress based on the statistical damage model under uniaxial tension. The damage evolution law in the direction subjected to pressure is confirmed by the tensile damage evolution process of lateral deformation due to the Poisson effect,and then the compressive stress-strain relationship is defined. The peak nominal stress state and the critical state occurring in the macro longitudinal distributed splitting cracks are distinguished. The whole loading process can be divided into the even damage phase and the local breakage phase. The concrete specimen is divided into the failure process zone and the resting unloading zone. The size effects during the local breakage phase under the uniaxial monotonic compressive process and the hysteretic phenomenon under the cyclic compressive loading process are analyzed. Finally,the comparison between theoretical results and experimental results preliminarily verifies the rationality and feasibility of understanding the failure mechanism of concrete through the statistical damage constitutional law.

HEAT-AFFECTED ZONE FRACTURE TOUGHNESS OF HIGH STRENGTH STEELS EVALUATED USING THE WEAKEST LINK MODEL

A probabilistic model is derived based on the weakest link theory to evaluate the specimen thickness effect and the size effect of coarse-grained heat-affected zone (CGHAZ) on CTOD toughness values in heat-affected zones (HAZ) of high strength steels. The scatter of CTOD fracture toughness values in heterogeneous weldments is predicted using this model. The specimen thickness has influence on the CTOD toughness values of HAZ. With increase in the specimen thickness the estimated and experimental mean CTOD values decrease while the lower boundary CTOD values remain almost unchanged. The size of CGHAZ has strong negative effect on the mean CTOD values of HAZ. The estimated mean CTOD values and lower boundary CTOD values agree with experimental CTOD testing results of HAZ notched specimens. The facture toughness scatter is dependent on the Weibull shape parameter a and specimen thickness.

Numerical study of anomalous dynamic scaling behaviour of (1+1)-dimensional Das Sarma-Tamborenea model

In order to discuss the finite-size effect and the anomalous dynamic scaling behaviour of Das Sarma-Tamborenea growth model, the （1＋1）-dimensional Das Sarma-Tamborenea model is simulated on a large length scale by using the kinetic Monte-Carlo method. In the simulation, noise reduction technique is used in order to eliminate the crossover effect. Our results show that due to the existence of the finite-size effect, the effective global roughness exponent of the （1＋1）-dimensional Das Sarma-Tamborenea model systematically decreases with system size L increasing when L 〉 256. This finding proves the conjecture by Aarao Reis[Aarao Reis F D A 2004 Phys. Rev. E 70 031607]. In addition, our simulation results also show that the Das Sarma-Tamborenea model in 1＋1 dimensions indeed exhibits intrinsic anomalous scaling behaviour.

TA1箔力学性能和断裂行为的尺寸效应

对不同晶粒尺寸的100μm厚TA1箔进行单轴拉伸试验,研究其力学性能和断裂行为的尺寸效应,并构建基于尺寸效应的微尺度本构方程。结果表明,随着晶粒尺寸增大,钛箔的拉伸应力及强度呈现增大的趋势,伸长率先缓慢下降至25%,随后快速降低。拉伸过程中颈缩阶段和平缓阶段不断缩短,除晶粒尺寸为56.88μm的试样外,其余试样断口夹角处于50°~60°,为典型的剪切型断裂。晶粒尺寸超过21.08μm后,断口表面的撕裂棱和韧窝数量不断减少,断裂模式由塑性断裂转变为准解理断裂,晶粒尺寸大于36.14μm后,钛箔基体从HCP-Ti结构转变为FCC-Ti结构,位错密度降低,断口表面出现明显的解理断裂特征,断裂模式完全转变为解理断裂。基于表面层模型构建考虑尺寸效应的本构模型,可精确预测微尺度钛箔拉伸过程中的力学特性。

置信区间宽度等高线图在线性混合效应模型样本量规划中的应用

线性混合效应模型在分析具有嵌套结构的心理学实验数据时具有明显优势。本文提出了置信区间宽度等高线图用于该模型的样本量规划。通过等高线图,确定同时符合检验力、效应量准确性以及置信区间宽度要求的被试量和试次数。结合关注被试内实验效应和被试变量调节效应的两类典型模型,通过两个模拟研究,采用基于蒙特卡洛模拟方法,探索效应量、随机效应大小和被试变量类型对置信区间宽度等高线图及样本量规划结果的影响。

小比尺条形基础承载力模型试验的尺寸效应研究

开展小比尺模型试验是土力学承载力研究中的重要方法,但小比尺模型的尺寸效应会影响试验的定量结果,导致小比尺试验一般仅能用于定性研究。在饱和砂土地基中开展了20组条形基础承载力的小比尺模型试验,通过改变基础尺寸、埋深以及砂土的密实度研究承载力的变化,进而引入离散元分析方法,采用抗转动模型模拟砂土颗粒的力学行为,对条形基础承载力试验进行模拟,从微观角度揭示小比尺模型试验尺寸效应的来源和对宏观承载力的影响规律。研究结果表明,饱和砂土地基密实度与基础埋深越大,小比尺实试验的尺寸效应越明显,尺寸效应的产生是应力水平变化、破坏模式改变以及渐进破坏程度综合作用的结果。

截面尺寸和箍筋对RC短柱抗震性能的影响

为了研究钢筋混凝土(reinforced concrete,RC)短柱的抗震性能,通过低周反复破坏试验对其抗震性能的尺寸效应进行了分析。试验主要考虑了截面尺寸和箍筋形式的影响,RC短柱的截面分别设计为200 mm×200 mm、400 mm×400 m和600 mm×600 mm,箍筋主要分为普通方形箍筋和井字箍筋。结果表明:配有普通方箍筋的RC短柱均表现出斜拉破坏特征,脆性破坏特征明显,而配有井字箍筋较大尺寸的RC短柱(边长为400 mm和600 mm)为剪压破坏;随着RC短柱截面边长的增加,其名义抗剪强度、延性和平均耗能系数均逐渐减小,并且配有井字箍筋的RC短柱相对于配有普通方形箍筋的短柱,其减小的速率逐渐变小。通过考虑截面尺寸和箍筋的影响作用,提出了修正的RC短柱的抗剪承载计算模型,并建立了考虑尺寸效应的RC短柱恢复力模型,计算结果与试验结果较吻合。

骨料含量和试件尺寸对混凝土单轴受压细观性能影响

为了研究粗骨料含量对混凝土单轴受压性能及尺寸效应的影响,通过编写Python脚本在Abaqus中建立二维混凝土随机骨料模型.该模型涵盖了骨料、砂浆和界面过渡区三相混凝土细观结构,使得模型更加接近真实混凝土结构;通过设置骨料含量和模型尺寸这两个变量,研究了其对模型力学性能的影响.研究结果表明,在同一试件尺寸下,随着骨料含量的增加,混凝土损伤破坏渐趋严重,弹性模量略有增大,抗压强度呈下降趋势;相同骨料含量下混凝土的尺寸效应明显,随着试件尺寸的增加,细观非均质性增强,导致混凝土抗压强度降低,损伤破坏现象更趋明显.分析尺寸效应对模型的影响规律,为实际情况下缩尺模型的性能预测提供参考.

考虑微裂纹随机分布的堆石颗粒准静态强度统计模型

材料内部裂纹尺寸、形状、转向和空间位置的随机分布对其强度有直接的影响。为了研究地震准静态荷载作用下堆石颗粒强度与尺寸和应变率的统计关系,在最弱链理论的框架下假设颗粒内部裂纹的尺寸和空间位置均服从幂律分布,建立了由颗粒累积破坏概率和体积构成的复合参数与强度的关系。从微观角度应变率效应提高了内部裂纹的强度,降低了单位体积的失效概率,同时使裂纹的空间位置分布更稀疏,减弱了颗粒强度的尺寸效应。不同加载速率的颗粒破碎试验结果表明:随着加载速率的增大,存在逐渐减小的空间分布幂指数使颗粒复合参数汇集在由最弱链统计模型决定的主曲线上。

激光选区熔化Ti-6Al-4V合金的微纳压痕尺寸效应

目的研究不同状态激光选区熔化Ti-6Al-4V合金的纳米压痕尺寸效应。方法对原始态合金分别进行600、700、800、900℃退火处理,利用扫描电子显微镜观察原始态和4种退火态合金的显微组织。基于纳米压痕技术测量原始态及4种退火态合金的纳米硬度和弹性模量。基于比例试样阻力模型、Nix-Gao模型和Meyer定律对纳米硬度进行函数拟合。结果随着退火温度的升高,原始态组织从魏氏体逐渐演变为网篮组织。5种形态的Ti-6Al-4V合金的硬度和弹性模量均出现随压入深度的增加而减小的现象,表现出典型的压痕尺寸效应,基于试验测得的原始态及4种退火态合金的纳米硬度分别为3.66、4.36、3.96、3.88、4.77 GPa,弹性模量分别为113.1、125.2、102.1、100.3、108.7 GPa;基于比例试样阻力模型计算的纳米硬度分别为3.53、4.34、3.92、3.52、4.04 GPa;基于Nix-Gao模型计算的纳米硬度分别为3.68、3.94、4.07、3.85、4.47 GPa;基于Meyer定律拟合出的迈耶指数分别为1.75、1.86、1.82、1.80、1.81,均小于2,均表现为正压痕尺寸效应。结论激光选区熔化Ti-6Al-4V合金的硬度及弹性模量均有典型的压痕尺寸效应;3种模型均能较好地描述原始态和退火态合金的压痕尺寸效应,Nix-Gao模型直接建立了纳米硬度和压痕深度的关系,其拟合结果更接近于试验结果,计算的硬度值也最为准确。

砂岩强度的动态尺寸效应机理研究

试验研究发现岩石强度的动态尺寸效应与静态尺寸效应相反,但岩石动态尺寸效应的内在微细观动力机理还没有澄清。本文以砂岩为例,基于岩石的翼状裂纹模型,联合求解裂纹的加载方程和运动方程,研究了在动载作用下试件尺寸对岩石强度的影响机理,即岩石强度的动态尺寸效应。结果表明:在相同动力加载率条件下,试件尺寸越大,裂纹连接所需要的时间越长;试件破坏时的施加的应力(也即动态强度)越大,试件的动态尺寸效应越显著,岩石动态强度近似以幂律关系增长;对于一定的试件尺寸范围,根据数值分析,得到岩石的临界应变率范围,在该临界应变率以下,静态的尺寸效应占主导地位,在该临界应变率以上,动态尺寸效应占主导地位,且临界应变率随试件尺寸增加而降低;试件临界尺寸随着应变率增加而降低。