Equivalent strain hardening exponent of anisotropic materials based on spherical indentation response

Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel method was proposed to estimate the equivalent strain hardening exponent of anisotropic materials based on an equivalent energy method. By performing extensive finite element (FE) simulations of the spherical indentation on anisotropic materials, dimensionless function was proposed to correlate the strain hardening exponent of anisotropic materials with the indentation imprint parameters. And then, a mathematic expression on the strain hardening exponent of anisotropic materials with the indentation imprint was established to estimate the equivalent strain hardening exponent of anisotropic materials by directly solving this dimensionless function. Additionally, Meyer equation was modified to determine the yield stress of anisotropic materials. The effectiveness and reliability of the new method were verified by the numerical examples and by its application on the TC1M engineering material.

A new method of characterizing equivalent strain for equal channel angular processing

In order to establish the quantitative relationship between equivalent strain and the performance index of the deformed material within the range of certain passes for equal channel angular processing （ECAP）, a new approach to characterize the equivalent strain was proposed. The results show that there exists better accordance between mechanical property （such as hardness or strength） and equivalent strain after rolling and ECAP in a certain range of deformation amount, and Gauss equation can be satisfied among the equivalent strain and the mechanical properties for ECAP. Through regression analysis on the data of hardness and strength after the deformation, a more generalized expression of equivalent strain for ECAP is proposed as：ε=k0exp[-（k1M-k2）^2], where M is the strength or hardness of the material, k1 is the modified coefficient （k1∈ （0, 1））, ko and k2 are two parameters dependent on the critical strain and mechanical property that reaches saturation state for the material, respectively. In this expression the equivalent strain for ECAP is characterized novelly through the mechanical parameter relating to material property rather than the classical geometry equation.

Calculation of the Distribution Rule of Equivalent Strain Rate near Explosive Welding Interface

The objectives of this study were to analyze the distribution of equivalent strain rate near the stagnation point and probe into the effects of colliding angle on strain rate. An ideal fluid model of symmetrically colliding was used to research them. Calculations showed the equivalent strain rate and the colliding half angle are closely related to each other with the material geometrical size and explosive velocity selected, the equivalent strain has large gradient within several jet thicknesses near the stagnation point, the maximal strain points are lined up along a beeline, but a curve near the stagnation point. With different colliding angles, they can be fitted by using exponential curve. That is, the exponential curve can be regarded as the token curve in explosive welding..

An Equivalent Strain Based Multi-Scale Damage Model of Concrete

A multi-scale damage model of concrete is proposed based on the concept of energy equivalent strain for generic two-or three-dimensional applications.Continuum damage mechanics serves as the framework to describe the basic damage variables,namely the tensile and compressive damage.The homogenized Helmholtz free energy is introduced as the bridge to link the micro-cell and macroscopic material.The crack propagation in micro-cells is modeled,and the Helmholtz free energy in the cracked micro-structure is calculated and employed to extract the damage evolution functions in the macroscopic material.Based on the damage energy release rates and damage consistent condition,the energy equivalent strain is used to expand the uniaxial damage model to the multi-dimensional damage model.Agreements with existing experimental data that include uniaxial tensile and compressive tests,biaxial compression and biaxial peak stress envelop demonstrate the capacity of the multi-scale damage model in reproducing the typical nonlinear performances of concrete specimens.The simulation of precast laminated concrete slab further demonstrates its application to concrete structures.

Multi-axial strain-stiffening elastic potentials with energy bounds:explicit approach based on uniaxial data

According to the well-known models for rubberlike elasticity with strain- stii^ening effects, the unbounded strain energy is generated with the unlimitedly growing stress when the stretch approaches certain limits. Toward a solution to this issue, an explicit approach is proposed to derive the multi-axial elastic potentials directly from the uniaxial potentials. Then, a new multi-axial potential is presented to characterize the strain-stiffening effect by prescribing suitable forms of uniaxia] potentials so that the strain energy is always bounded as the stress grows to infinity. Numerical examples show good agreement with a number of test data.

New correlations for evaluating the equivalent bare charge mass for a cased charge

Munitions contain casings that consume explosive energy.The blast load(e.g.,peak overpressure and maximum impulse)intensity generated by ammunition explosion will be lower than that generated by a bare charge with equal mass.To evaluate the blast load of a cased charge under different conditions,the equivalent bare mass needs to be calculated.However,the accuracy of existing correlations strongly depends on the empirical determination of relevant controlling parameters and lacks theoretical clarification.In this paper,new correlations are proposed based on a more rigorous theoretical derivation,considering both the mechanical behaviors of the casing’s material and the change of the polytropic exponent during the expansion process of the explosion products.The controlling parameters are attributed to the rupture radius ratio and the polytropic exponent of detonation products expansion to casing rupture state.The reasonability is validated by both comprehensive numerical simulations with dynamic mechanical constitutive model and theoretical derivations.The results calculated by the new correlation show better agreement with the experimental results than those calculated by previous correlations,and the results difference is explained in more consistency with the thermos-physical properties of the charge and mechanical behaviors of casing material.Furthermore,the correlation of the cased-to-bare impulse ratio is also theoretically improved,providing a more accurate theoretical basis for both the equivalent bare mass and impulse evaluation for a cased charge.

APPLICABILITY OF DAMAGE DEFINITION BASED ON HYPOTHESIS OF STRAIN EQUIVALENCE

The hypothesis of strain equivalence is used to measure damage in materials. The physical meaning of the elastic modulus of damaged materials defined in the hypothesis is discussed in this paper. The inapplicability of the hypothesis to be used to determine the damage and its evolution in elasto plastic materials are analyzed. It is emphasized that the method in which the relaxed modulus is taken as the deformed modulus, i.e. the elastic modulus defined in the hypothesis, is only applicable for measuring the damage in elastic materials. A new damage variable is proposed, which is applicable for both elastic and elastoplastic materials.

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.

STRAIN ANALYSIS OF LATERAL EXTRUSION PROCESS

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Advanced test methods of material property characterization:high strain-rate testing and experimental simulation of multiaxial stress states

Optimum utilization of the loading capability of engineering materials is an important and active contribution to protect nature's limited resources,and it is the key for economic design methods.In order to make use of the materials' resources,those must be known very well;but conventional test methods will offer only limited informational value.The range of questions raised is as wide as the application of engineering materials,and partially they are very specific.The development of huge computer powers enables numeric modelling to simulate structural behaviour in rather complex loading environments-so the real material behaviour is known under the given loading conditions.Here the art of material testing design starts.To study the material behaviour under very distinct and specific loading conditions makes it necessary to simulate different temperature ranges,loading speeds, environments etc.and mostly there doesn't exist any commonly agreed test standard.In this contribution two popular,non-standard test procedures and test systems will be discussed on the base of their application background,special design features as well as test results and typically gained information:The demand for highspeed tests up to 1000 s^(-1) of strain rate is very specific and originates primarily in the automotive industry and the answers enable CAE analysis of crashworthiness of vehicle structures under crash conditions.The information on the material behaviour under multiaxial loading conditions is a more general one.Multiaxial stress states can be reduced to an equivalent stress,which allows the evaluation of the material's constraint and criticality of stress state.Both discussed examples shall show that the open dialogue between the user and the producer of testing machines allows custom-tailored test solutions.

RPC应力-应变曲线系数与塑性损伤因子无量纲化计算模型研究

为了方便活性粉末混凝土(Reactive Powder Concrete,RPC)等效矩形应力图系数与塑性损伤因子的计算与取值,对RPC应力-应变曲线系数与塑性损伤因子的计算模型进行了理论研究。通过对现有的计算方法进行无量纲化转化,推导了决定计算模型的四个原函数条件;对一个实际的应力-应变关系进行了计算,将得到的结果进行了分析;并对受弯矩形梁非极限状态下截面内力和力矩的推定计算进行了演示。针对应力-应变关系式含有非整次有理分式的情况提出了曲线拟合方法;研究了拟合次数、拟合区间和拟合函数类型对拟合精度与稳定性的影响。比较了4种典型的RPC本构模型在同种材料下的应力-应变曲线系数与损伤因子取值模型曲线,结果显示:拟合曲线得到的取值模型与其他原始曲线得到的取值模型在曲线上具有较高的相似度,证明了曲线拟合方法的准确可靠性;最后给出了一种RPC受压应力-应变曲线系数与塑性损伤因子无量纲化取值模型。

钢-混组合梁荷载-温度效应的统一解析模型

基于欧拉伯努利梁理论,提出非均布荷载、轴向力、梁端弯矩和非线性温度分布共同作用下的有滑移组合梁统一解析模型,推导组合梁挠度、界面剪力、滑移及截面应力的计算公式,开展简支组合梁和连续组合梁算例分析,讨论界面刚度和温度作用对界面滑移和挠度的影响.研究结果表明,组合梁温度作用产生的挠度与界面滑移由等效温度滑移应变和等效温度曲率决定,可以通过将桥面板与钢梁的温度分布各自分解为有效温度、竖向线性温差和残余温度等相互独立的3部分进行计算.简支梁和2跨连续梁算例在温度作用下的界面滑移沿梁长呈现反对称分布,滑移主要集中在距端部小于2 m的范围内,受滑移的影响,组合梁端部桥面板底面的拉应力水平较高,可以超过2 MPa,增加了底面混凝土开裂的风险.提出了温度作用下界面滑移组合梁的挠度影响系数,可以用于组合梁挠度的快速计算,其大小不仅与界面完全连接与界面无连接时组合梁的抗弯刚度比和组合效应系数有关,还受温度作用系数的直接影响.

波形钢腹板工字梁的等效计算模型及稳定性分析

基于变形与应变能相等的原则,提出波形钢腹板工字梁的等效平直钢腹板计算模型。通过波形钢腹板直板段与斜板段应变分析,推导了波形钢腹板工字梁及等效计算模型的应变能,建立等效惯性矩与等效扇性惯性矩,利用平直钢腹板工字梁的临界荷载计算公式,对波形钢腹板工字梁进行稳定性分析。研究结果表明:该方法简单、便捷,对波形钢腹板工字梁的稳定分析准确、有效;建立的等效惯性矩与翘曲惯性矩仅取决于截面及波形钢板尺寸,不受工字梁的边界条件、跨径等因素的影响,具有良好的适应性。

单调与循环载荷下多晶纯铜局部取向差演化数值模拟

为了揭示不同载荷下局部取向差的演化规律及其与变形损伤的关系,选取多晶纯铜为研究对象,基于DAMASK晶体塑性有限元的开源软件及Python脚本代码编写软件,研究了多晶纯铜在单调拉伸与循环载荷下的晶粒内取向差(KAM)、晶粒参考取向偏差(GROD)与等效塑性应变的演化规律,并采用取向差频率分布与相关系数评估了KAM与GROD表征变形损伤的优劣。结果表明:单调拉伸与循环载荷下KAM、GROD与等效塑性应变峰值区域分布一致,高取向差和高塑性区域首先出现在晶界或者三叉晶界附近,且取向差与宏观等效塑性应变呈线性正相关。单调拉伸和循环加载下GROD的频谱相似,而KAM的频谱对载荷敏感且相关系数更高,能更好地表征变形损伤。

Al/Ti异质合金回填式搅拌摩擦点焊数值模拟

采用耦合的欧拉-拉格朗日(CEL)算法对2 mm厚的5A02铝合金/TC4钛合金板异质金属回填式搅拌摩擦点焊过程展开模拟研究,分析了旋转速度和停留时间对焊点成型过程中温度场、等效塑性应变场以及材料流动的影响。结果表明,在扎入初期,热累积作用明显,升温速率相对较快,随焊接过程进行,产热会由摩擦产热转变为摩擦和塑性变形共同产热,升温速率放缓。当搅拌头转速为2000 r/min、扎入速度为1 mm/s、扎入深度为1.9 mm、回填速度为1mm/s、停留时间为0 s时,铝合金焊核区温度峰值达到558℃,等效塑性应变峰值达到120。在模拟的工艺区间内,焊核区峰值温度与旋转速度呈正相关,停留时间对温度的影响并不明显。

2205/Q420/2205蛇形轧制复合变形规律研究

为研究三层不锈钢复合板在不同工艺参数下轧制复合的变形规律,采用ANSYS有限元软件模拟了2205/Q420/2205三层复合板轧制复合过程,研究了同步轧制、同速异径轧制和同速异径蛇形轧制三种不同工艺下,复合板结合界面等效塑性应变和弯曲曲率的变化规律,分析了不同压下率、初始厚度比和错位量对轧后板形的影响规律,并进行了轧制复合实验。研究结果表明,蛇形轧制通过调整错位量,能有效提高轧后板材界面结合强度并降低轧后弯曲。轧后弯曲曲率随着压下率的增大呈现出先减小后增大的趋势。等效塑性应变随着错位量的增加先增大后减小,轧后弯曲曲率随着错位量的增加逐渐降低,这表明通过适当调整错位量可以使轧后板材同时达到优良的结合强度和平直度。

海上风电单柱复合筒型基础复合加载条件下的承载特性

为研究新型海上风电单柱复合筒型基础在二维复合加载条件下的承载特性,利用有限元模型计算,首先得到模型在一维荷载空间下的极限承载力,随后通过施加不同的竖向荷载,得到在V-H、V-M、V-H-M荷载空间下的承载能力包络图,并分析不同二维荷载工况下的单柱复合筒型基础各位置处的土压力分布情况以及筒体底部等效塑性应变区的变化情况。结果表明:对于单柱复合筒型基础,在一定范围内,竖向荷载(0~0.15倍竖向极限承载力)的存在能够增大结构的水平及弯矩承载力;在V-H与V-M荷载空间中,基础各位置处的土压力变化、土体等效塑性应变变化具有一定的相似性,可互相对映参考;基础所承受的最大土压力位置与基础受力倾倒方向一致;随着竖向荷载的增加,结构达到极限承载力时,基础底部土体等效塑性应变区的范围与深度相应扩大。

饱和珊瑚砂体应变发展模式与预测模型试验研究

珊瑚砂具有较好的排水条件,地震、波浪荷载作用下饱和珊瑚砂产生的排水变形易引起海床和附近结构物的破坏。利用GDS循环三轴仪,针对南沙岛礁饱和珊瑚砂试样进行了一系列循环排水加载试验,以探究细粒含量FC、相对密度D_r及循环应力比CSR对饱和珊瑚砂变形特性的影响。试验结果表明,饱和珊瑚砂的累积体应变ε_(vp)的发展速率和变形程度随FC、CSR的增大而增大,随D_(r)的增大而减小。饱和珊瑚砂ε_(vp)-N关系曲线呈现出循环平稳和循环蠕变两种发展模式。引入潜在破坏系数DP表征FC对ε_(vp)发展模式的影响,建立了DP×CSR-D_(r)框架的饱和珊瑚砂体应变发展模式评价方法。为表征FC及D_(r)对饱和珊瑚砂ε_(vp)-N关系曲线的影响,引入了骨架孔隙比e_(sk)*,发现两种发展模式下ε_(vp-s)与e_(sk)*均存在良好的相关性,遂建立了排水循环加载条件下饱和珊瑚砂的体应变发展模型,可以较好地预测饱和珊瑚砂的累积体应变发展规律。

圆锥滚子轴承套圈辗扩成形有限元模拟

环件辗扩是轴承套圈的主要成形方法,加工质量直接影响轴承的使用性能。以圆锥滚子轴承为例,基于DEFORM建立套圈径向辗扩有限元模型,通过试验验证了模型的正确性,并分析了初始辗扩温度、芯辊进给速度和主动辊转速对套圈等效应变和温度的影响,结果表明:初始辗扩温度、芯辊进给速度增大,套圈等效应变减小;主动辊转速增大会使套圈等效应变增加;芯辊进给速度和主动辊转速增大,套圈温度升高且温度分布更均匀。

铝合金深冷挤压切削加工有限元仿真及实验研究

目的为提升大变形技术的加工效率和质量,消除变形热带来的影响,提出一种基于传统切削的深冷挤压切削(Cryogenic Temperature Extrusion Machining,CT-EM)工艺,并通过数值模拟与实验验证了该方法的可靠性。方法利用DEFORM软件中的点追踪与流动网格法对不同切削压缩比(1.4、1.6、1.8)条件下的等效应变、应变率及切屑成形过程进行了有限元模拟,开展了切削实验,并对切屑的形貌及微观组织进行了分析。结果挤压切削分为初始切入、切屑成形以及稳定成形3个阶段,第二变形区的网格畸变最严重;等效应变随着压缩比的增大而增大,其值在1.2~1.6之间,与计算值较吻合;等效应变率产生于第一变形区宽度为200~250μm的区域,且CT-EM具有更高的等效应变率;CT-EM制备的切屑带材表面粗糙度低、裂纹少、成形能力更优,切屑内的微观组织被强烈细化(<200 nm),达到了超细晶结构,且产生了大量的位错缠结区。结论深冷处理可提升7系铝合金切削加工时的成形能力,晶粒细化是较大的等效应变与应变率共同作用的结果,模拟数据对实验结果有较好的支撑。