正交各向异性Kagome蜂窝材料宏观等效力学性能

由于微结构的布局和尺寸的方向性,人造和天然的蜂窝材料都会不同程度呈现各向异性,其中正交各向异性的蜂窝材料较为常见.该文采用桁架模型推导了正交各向异性Kagome单胞蜂窝材料等效刚度和强度的解析表达式,给出了初始屈服函数和近似弹性屈曲强度,讨论了等效刚度与各向异性率和相对密度的关系.等效刚度的解析结果与单胞壁杆采用梁单元建模的刚架模型均匀化结果进行比较,结果令人满意.需要说明的是这类"组合蜂窝"材料具有多功能性和潜在的可设计性,正在受到人们关注.     

基于非关联流动规律的Gotoh屈服准则的参数确定方法

屈服准则对板料成形过程的理论解析、工艺优化和有限元模拟有着重要的影响. 通过提高屈服准则的各向异性表征能力, 可以确保成形过程的可靠性及实际预测的准确性. 本文基于非关联流动法则, 给出了Gotoh屈服准则一套全新的参数求解方法. 在结合常用屈服准则并考虑流动规律的基础上, 分别以5754O铝合金、DP980先进高强钢和SAPH440结构钢作为研究对象, 进行了不同加载路径下各向异性变形行为的预测. 根据Gotoh屈服准则推导的屈服函数、塑性势函数以及基于关联流动的理论函数计算出屈服应力和各向异性指数$r$值随加载角度的分布趋势, 进而针对平面应力状态的屈服轨迹展开分析, 验证了不同屈服准则和流动规律对各向异性屈服行为的预测精度. 理论与实验数据对比结果表明: 不同屈服准则针对同种板料在流动规律一致的情形下其表征各向异性的能力有显著差异; 相同屈服准则基于不同流动规律其表征能力也具有明显差别. 基于非关联流动的屈服准则能极大地提高精度, 各向异性表征能力显著加强. 相关结果能够为各向异性屈服准则在塑性成形领域的实际应用方案提供重要参考.      

基于非关联流动规律的Gotoh屈服准则的参数确定方法

屈服准则对板料成形过程的理论解析、工艺优化和有限元模拟有着重要的影响.通过提高屈服准则的各向异性表征能力,可以确保成形过程的可靠性及实际预测的准确性.本文基于非关联流动法则,给出了Gotoh屈服准则一套全新的参数求解方法.在结合常用屈服准则并考虑流动规律的基础上,分别以5754O铝合金、DP980先进高强钢和SAPH440结构钢作为研究对象,进行了不同加载路径下各向异性变形行为的预测.根据Gotoh屈服准则推导的屈服函数、塑性势函数以及基于关联流动的理论函数计算出屈服应力和各向异性指数r值随加载角度的分布趋势,进而针对平面应力状态的屈服轨迹展开分析,验证了不同屈服准则和流动规律对各向异性屈服行为的预测精度.理论与实验数据对比结果表明:不同屈服准则针对同种板料在流动规律一致的情形下其表征各向异性的能力有显著差异;相同屈服准则基于不同流动规律其表征能力也具有明显差别.基于非关联流动的屈服准则能极大地提高精度,各向异性表征能力显著加强.相关结果能够为各向异性屈服准则在塑性成形领域的实际应用方案提供重要参考.     

准脆性材料的弹塑性各向异性损伤耦合本构模型研究

针对准脆性材料的非线性特征：强度软化和刚度退化、单边效应、侧限强化和拉压软化、不可恢复变形、剪胀及非弹性体胀,在热动力学框架内,建立了准脆性材料的弹塑性与各向异性损伤耦合的本构关系。对准脆性材料的变形机理和损伤诱发的各向异性进行了诠释,并给出了损伤构形和有效构形中各物理量之间的关系。在有效应力空间内,建立了塑性屈服准则、拉压不同的塑性随动强化法则和各向同性强化法则。在损伤构形中,采用应变能释放率,建立了拉压损伤准则、拉压不同的损伤随动强化法则和各向同性强化法则。基于塑性屈服准则和损伤准则,构建了塑性势泛函和损伤势泛函,并由正交性法则,给出了塑性和损伤强化效应内变量的演化规律,同时,联立塑性屈服面和损伤加载面,给出了塑性流动和损伤演化内变量的演化法则。将损伤力学和塑性力学结合起来,建立了应变驱动的应力-应变增量本构关系,给出了本构数值积分的要点。以单轴加载-卸载往复试验识别和校准了本构材料常数,并对单轴单调试验、单轴加载-卸载往复试验、二轴受压、二轴拉压试验和三轴受压试验进行了预测,并与试验结果作了比较,结果表明,所建本构模型对准脆性材料的非线性材料性能有良好的预测能力。     

聚氨酯高聚物注浆材料剪切测试与有限元模拟

通过扭转试验对高聚物注浆材料剪切性能进行试验研究,并在扫描电子显微镜(scanning electron microscope, SEM)下观测了试件断面处胞体形状破坏特征,在此基础上通过有限元数值模拟,对其剪切变形力学响应特征及剪应力分布规律进行了研究。结果表明:密度对高聚物材料的剪切强度及剪切模量影响显著,且随着高聚物材料密度的增加,其剪切强度和剪切模量被显著提升;高聚物材料胞体分布遵循能量最低原理,密度越大,胞体表面积越小,表面能越小,体系越稳定;面心立方体堆砌模型可以较好模拟材料剪切变形行为,且密度越大,拟合效果越好。     

PREDICTIONS OF EFFECTIVE OUT-PLANE SHEAR MODULUS AND SIZE EFFECT OF HEXAGONAL HONEYCOMB

给出了预测六边形蜂窝材料等效剪切模量及其尺寸效应的圆筒扭转力学模型和扭转能量法,建立了等效面外剪切模量G₁₃相对于材料体分比ν、周向单胞数n、圆筒半径r和单胞层数参数m变化的解析表达式;同时将扭转能量法、有限元数值模拟计算和G-A经典细观力学方法进行了比较,从理论上揭示并验证了尺寸效应的存在性. 结果表明,当蜂窝体胞尺寸相对结构尺寸无穷小时,预测结果趋近于细观力学方法的结果. 此外,利用周期性蜂窝材料的结构对称特性,使用体胞子结构有限元计算模型进行等效面外剪切模量及其尺寸效应的预测,在不影响计算结果的前提下极大地提高了计算效率.     

[100]LiF单晶在60 GPa以内冲击加载下的高压屈服强度特性

获取光学窗口自身的高压强度特性是开展材料高压高应变率冲击响应行为精密测量和数据反演的重要基础。利用平板撞击和双屈服面法,通过冲击-卸载、冲击-再加载原位粒子速度剖面精细测量和数据反演,获得了约60 GPa范围内[100]LiF屈服强度特性随冲击压力的变化规律。结果表明:在实验压力范围内,[100]LiF的屈服强度随加载压力的提高而显著提高,压力硬化效应显著;同时,LiF在冲击加载下的屈服强度高于磁驱准等熵加载结果,应变率硬化效应强于热软化效应。采用Huang-Asay模型确定了可描述冲击加载[100]LiF强度特性的本构模型参数,为LiF在强度、相变、层断裂等加窗测量实验中的深入应用和数据准确解读提供了重要支撑。     

蜂窝材料的非线性剪切行为

将梁的弹性大挠度弯曲理论应用于蜂窝壁板,研究了大变形条件下蜂窝材料的非线性剪切变形行为．研究中将椭圆积分形式的解答应用于蜂窝胞元的壁板,并利用平衡和变形谐调条件建立了相应的非线性代数方程组,然后利用牛顿-拉夫森迭代法求解．在上述数值解法的基础上,确定了等效剪应力和剪应变间的非线性曲线,并给出了剪切模量的非线性修正因子,该因子只与蜂窝形状和变形情况有关,而与细长比无关,因而能描述一类蜂窝材料的剪切行为．与有限元数值结果的比较表明,此方法具有较好的精度．     

零泊松比手风琴蜂窝等效模量

柔性蒙皮是变形机翼和风力机叶片的关键组成部分。一维变形的柔性蒙皮不仅要求其支撑结构具有良好的面内变形和面外承载能力,还需要具有零泊松比特性。手风琴蜂窝具有零泊松比特性,可用作一维变形柔性蒙皮支撑。为全面分析其面内外弹性变形特性,综合考虑结构的内力弯矩、轴力和剪力,通过卡氏第二定理对其x向等效弹性模量和x-y面内等效剪切模量进行了推导;利用最小余能原理和最小势能原理确定了x-z面内的等效剪切模量;此外还推导了其y和z向的等效弹性模量以及y-z面内的等效剪切模量;然后通过ANSYS有限元仿真对等效模量理论公式进行了验证;最后将本文理论模型与现有模型进行了比较。结果表明,理论公式和有限元仿真吻合较好,在结构设计时采用较大的斜梁高度系数h和斜梁间距系数g,较小的厚度系数t以及较大的竖直梁厚度系数η,有望获得具有较小面内刚度和较大面外刚度的手风琴蜂窝结构。该结果可用于手风琴蜂窝面内外等效模量的快速预测,为一维变形柔性蒙皮的结构设计提供相应的参考。此外,本文理论模型相比传统模型更为精确且具有更加广泛的应用范围。     

动载荷下材料的屈服强度变化

描述了冲击加载和准等熵加载下获得材料动态屈服强度的方法,并以钨合金材料为研究对象,通过VISAR测试技术测量了钨合金材料在冲击加载下的屈服强度随压力的变化,并把实验结果与文献报道的准等熵加载下的材料强度变化的实测结果进行了比较。结果表明,准等熵加载下材料的屈服强度明显高于冲击加载下的材料屈服强度,并认为这主要是由于两种加载方式下材料的温升效应不同所造成的。     

关于蜂窝芯体面外等效剪切模量的讨论

对于六边形蜂窝芯体,其面内等效参数具有确定的解析式,便于应用;相比之下,对于面外等效剪切模量,现有工作只能给出其上下限,由于没有确定的取值,给工程计算带来了困扰。为克服这一矛盾,本文通过Y型蜂窝胞元,针对薄面板的情况,重新分析了芯材的面外等效剪切模量。针对直壁板与斜壁板厚度为1:1和2:1的情况,给出了近似的弹性力学解答,并由此确定出面外等效剪切模量的上限。本方法所确定的剪切模量的上限与文献给出的剪切模量的下限是相同的,从而使该模量也具有确定的解析表达式,方便了数值计算和分析。试验数据和有限元数值分析均验证了本文结论的正确性。     

Quasi-static crush behavior of aluminum honeycomb specimens under non-proportional compression-dominant combined loads

The quasi-static crush behavior of aluminum 5052-H38 honeycomb specimens under non-proportional compression-dominant combined loads is investigated by experiments. A test fixture was designed such that dominant compressive and shear loads with respect to the strongest material symmetry direction can be controlled and applied independently. Compression-dominant combined loads and pure compressive loads were applied in different sequences to induce non-proportional combined loads. The experimental results show that the normal crush and shear strengths in combined loading regions and the normal crush strengths in pure compressive loading regions of the non-proportional combined loads are quite consistent with the existing phenomenological yield criterion based on the experimental normal crush and shear strengths under proportional combined loads. The experimental results also indicate that the sequence of loading paths for the non-proportional combined loads does not affect the crush strengths when compared with those obtained under proportional combined loads. In addition, the experimental results indicate that the non-normality plastic flow behavior of honeycomb specimens under non-proportional combined loads is consistent with that under proportional combined loads. Finally, specimens crushed under non-proportional combined loads show developments of different stacking patterns of folds in different loading regions of the non-proportional combined loads. The experimental results suggest that the incremental stress–strain relation for the transition loading path within the so-called yield surface from one yield state to another may be related to the displacement increments that correspond to the change of microscopic folding mechanisms instead of the usual elastic relation according to the classical plasticity theory.     

Dynamic crush behaviors of aluminum honeycomb specimens under compression dominant inclined loads

The dynamic crush behaviors of aluminum 5052-H38 honeycomb specimens under compression dominant inclined loads are investigated by experiments. Different types of honeycomb specimens were designed for crush tests under pure compressive and compression dominant inclined loads with respect to the out-of-plane direction. A test fixture was designed for dynamic crush tests under inclined loads. The results of the dynamic crush tests indicate that as the impact velocity increases, the normal crush strength increases and the shear strength remains nearly the same. The trends of the normalized normal crush strengths under inclined loads for specimens with different in-plane orientation angles as functions of the impact velocity are very similar to each other. Based on the experimental results, a macroscopic yield criterion as a function of the impact velocity is proposed. The experimental results suggest that, as the impact velocity increases, the shape of the macroscopic yield surface changes, or more specifically, the curvature of the yield surface increases near the pure compression state. The experimental results also show similar microscopic progressive folding mechanisms in honeycomb specimens under pure compressive and inclined loads. However, honeycomb specimens under inclined loads show inclined stacking patterns of folds due to the asymmetric location of horizontal plastic hinge lines.     

Quasi-static crush behavior of aluminum honeycomb specimens under compression dominant combined loads

The influence of shear stress on the quasi-static crush behavior of aluminum honeycomb specimens under compression dominant combined loads is investigated by experiments. A test fixture was designed such that dominant compressive and shear loads with respect to the strongest material symmetry direction can be controlled and applied independently. Honeycomb specimens were also designed such that the secondary non-uniform stresses due to the stress-free boundary can be minimized. The experimental results indicate that the normal crush strengths under combined compressive and shear loads are lower than that under pure compressive loads. A phenomenological yield criterion for specimens with different in-plane orientation angles is proposed based on the experimental normal crush and shear strengths under combined loads. The experimental results suggest non-normality plastic flow based on the yield criterion. The non-normality flow behavior becomes more pronounced as the in-plane orientation angle increases. The experimental results also indicate that the energy absorption rate depends upon the ratio of the shear stress to the compressive stress and the in-plane orientation angle. In addition, specimens crushed under combined loads show inclined stacking patterns of folds due to the asymmetric location of horizontal plastic hinge lines and the rupture of aluminum cell walls along the adhesive lines. These experimental observations are useful to develop microscopic plasticity models of aluminum honeycombs under compression dominant combined loads.     

Yield surfaces of various periodic metal honeycombs at intermediate relative density

Initial yield surfaces are derived for several periodic metal honeycomb cell structures with sufficiently high relative density that failure occurs by plastic yielding. Both in-plane stress states (normal stresses perpendicular to cell axes, with in-plane shear) and triaxial stress states with one principal stress direction along the cell axes are considered. Beam/column and plate/shell yield criteria are adopted to address general in-plane loading and 3D triaxial loading, respectively, accounting for combined cell wall stretching and bending as appropriate. Cell wall behavior is assumed to be elastic-perfectly plastic. The initial yield surfaces for different periodic cell structures are systematically compared. Some issues related to the initial yield surfaces of various honeycombs are discussed, including dependencies on relative density and in-plane and out-of-plane applied stresses, as well as the influence of joints between cell walls.     

Mechanical Properties of two novel planar lattice structures

Two novel statically indeterminate planar lattice materials are designed: a new Kagome cell (N-Kagome) and a statically indeterminate square cell (SI-square). Their in-plane mechanical properties, such as stiffness, yielding, buckling and collapse mechanisms are investigated by analytical methods. The analytical stiffness is also verified by means of finite element (FE) simulations. In the case of uniaxial loading, effective modulus, yield strength, buckling strength and critical relative density are compared for various lattice structures. At a critical relative density, the collapse mode will change from buckling to yielding. Elastic buckling under macroscopic shear loading is found to have significant influence on failure of lattice structures, especially at low relative densities. Comparison of the analytical bulk and shear moduli with the Hashin–Shtrikman bounds indicates that the mechanical properties of the SI-square honeycomb are relatively close to being optimal. It is found that compared with the other existing stretching-dominated 2D lattice structures, the N-Kagome cell possesses the largest continuous cavities for fixed relative densities and wall thicknesses, which is convenient for oil storage, disposal of heat exchanger, battery deploying and for other functions. And the initial yield strength of the N-Kagome cell is slightly lower than that of the Kagome cell. The SI-square cell has similar high stiffness and strength as the mixed cell while its buckling resistance is about twice than that of the mixed cell.     

关于蜂窝结构面内剪切模量的注记

本文指出Gibson等提出的等壁厚峰窝结构在面内剪力作用下的单元分析不满足平衡条件.本文建立了等壁厚与非等壁厚峰窝结构在面内剪力作用下的合理的单元分析,导出了蜂窝结构面内折合剪切模量G_(xy)的计算公式.本文结果与实验数据符合得很好.     

FE analysis of the in-plane mechanical properties of a novel Voronoi-type lattice with positive and negative Poisson’s ratio configurations

This work presents a novel formulation for a Voronoi-type cellular material with in-plane anisotropic behaviour, showing global positive and negative Poisson’s ratio effects under uniaxial tensile loading. The effects of the cell geometry and relative density over the global stiffness, equivalent in-plane Poisson’s ratios and shear modulus of the Voronoi-type structure are evaluated with a parametric analysis. Empirical formulas are identified to reproduce the mechanical trends of the equivalent homogeneous orthotropic material representing the Voronoi-type structure and its geometry parameters.     

APPLICATION AND THEORETICAL ANALYSIS OF C/SiC COMPOSITES BASED ON CONTINUUM DAMAGE MECHANICS

Based on the thermodynamic theory, an orthotropic damage constitutive model was developed to describe the nonlinear mechanical behavior of C/SiC composites. The different nonlinear kinematic and isotropic hardening functions were adopted to describe accurately the damage evolution processes. The damage variables were defined with the damaged modulus and the initial undamaged modulus on energy equivalence principle. The initial orthotropy and damage coupling were presented in the damage yield function. Tensile and in-plane shear loading and unloading tests were performed, and a good agreement between the model and the experimental results was achieved.