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再生砖混骨料混凝土基本力学性能与本构模型

朱超, 赵文韬, 余伟航, 刘超

朱超, 赵文韬, 余伟航, 等. 再生砖混骨料混凝土基本力学性能与本构模型[J]. 复合材料学报, 2024, 41(2): 898-910. DOI: 10.13801/j.cnki.fhclxb.20230531.004
引用本文: 朱超, 赵文韬, 余伟航, 等. 再生砖混骨料混凝土基本力学性能与本构模型[J]. 复合材料学报, 2024, 41(2): 898-910. DOI: 10.13801/j.cnki.fhclxb.20230531.004
ZHU Chao, ZHAO Wentao, YU Weihang, et al. Basic mechanical properties and constitutive model of recycled brick-concrete aggregate[J]. Acta Materiae Compositae Sinica, 2024, 41(2): 898-910. DOI: 10.13801/j.cnki.fhclxb.20230531.004
Citation: ZHU Chao, ZHAO Wentao, YU Weihang, et al. Basic mechanical properties and constitutive model of recycled brick-concrete aggregate[J]. Acta Materiae Compositae Sinica, 2024, 41(2): 898-910. DOI: 10.13801/j.cnki.fhclxb.20230531.004

再生砖混骨料混凝土基本力学性能与本构模型

基金项目: 国家自然科学基金(52178251);陕西省杰出青年科学基金项目(2020JC-46);中国博士后科学基金(2022MD713789);陕西省自然科学基础研究计划(2022JQ-343)
详细信息
    通讯作者:

    刘超,博士,教授,研究方向为再生混凝土材料及其结构性能 E-mail: chaoliu@xauat.edu.cn

  • 中图分类号: TB332

Basic mechanical properties and constitutive model of recycled brick-concrete aggregate

Funds: National Natural Science Foundation of China (52178251); Science Foundation Project for Outstanding Youth of Shaanxi Province (2020JC-46); China Postdoctoral Science Foundation (2022MD713789); Natural Science Basic Research Program of Shaanxi Province (2022JQ-343)
  • 摘要: 再生混凝土骨料中往往会混有再生砖骨料难以分离,将再生砖与再生混凝土骨料混合利用更加符合实际情况。本文以不同水胶比(0.3和0.4)、不同再生骨料取代率(体积法取代0%、50%、100%)为控制参数,研究了8组不同配合比的再生砖混骨料混凝土的抗压、劈裂抗拉、抗折和棱柱体抗压强度及单轴受压应力-应变关系。结果表明:与天然骨料混凝土相比,不同配合比再生混凝土力学性能有不同程度的下降,其中随着再生砖骨料含量的增加,其力学性能下降较显著,砖骨料替代率达到100%时抗压强度下降高达29.9%,但是仍能保证一定的力学性能储备。文中探究了水胶比与再生砖骨料掺量对混凝土力学性能的影响机制,并以试验数据为基础,建立了再生砖混骨料混凝土单轴受压本构模型和再生砖混骨料混凝土力学性能换算公式,研究结果可对此类再生混凝土结构的分析与设计提供参考。

     

    Abstract: Recycled concrete aggregate is often mixed with recycled brick aggregate, which is difficult to separate. The mixed use of recycled brick and recycled concrete aggregate is more in line with the actual situation. Different water-binder ratios (0.3 and 0.4) and different recycled aggregate replacement rates (0%, 50%, 100% replaced by volume method) were used as control parameters to study the compressive strength, splitting tensile strength, flexural strength, prism compressive strength and uniaxial compressive stress-strain relationship of eight groups of recycled brick-concrete aggregate concrete with different mix ratios. The results show that compared with natural aggregate concrete, the mechanical properties of recycled concrete with different mix ratios decrease to varying degrees. With the increase of recycled brick aggregate content, the mechanical properties decrease significantly. When the replacement rate of brick aggregate reaches 100%, the compressive strength decreases by up to 29.9%, but it can still ensure a certain mechanical property reserve. In this paper, the influence mechanism of water-binder ratio and recycled brick aggregate content on the mechanical properties of concrete is explored. Based on the experimental data, the uniaxial compression constitutive model of recycled brick concrete and the conversion formula of mechanical properties of recycled brick concrete are established. The research results can provide reference for the analysis and design of such recycled concrete structures.

     

  • 近年来由于航空航天、高铁的飞速发展,航空航天器、高速列车等在高速运行时会产生剧烈的振动,该结构的减振设计将成为技术的关键。波纹夹芯结构作为一种新型的复合材料组合结构,具有高比强度、高比刚度、质量轻、吸能能力强、承载效率高等良好特性,在航空航天、高速列车、汽车、建筑、机械、船舶等领域有着广泛的应用[1-4]。与传统的复合结构材料相比,波纹夹芯板结构很好地克服了夹芯板不连续的问题,具有良好的承载性能。此外,波纹夹芯板芯层间隙具备一定的流通性能,在间隙中穿插泡沫、多孔纤维、玻璃纤维等材料还能起到一定的隔声和隔热作用。因此,对波纹夹芯板的研究具有重要的意义。

    由于夹层板拥有广阔的应用前景,近年来国内外学者针对波纹夹芯板各方面特性展开了广泛的研究。Peng等[5] 提出一种无网格伽辽金法来研究非加筋和加筋波纹夹芯板的弹性弯曲问题,将波纹夹芯板视为在两个垂直方向上具有不同挠曲力的正交各项异性板,并推导了梯形、正弦型波纹夹芯板的等效参数。Semenyuk等[6]研究了三种用于纵向波纹圆柱壳稳定性分析的设计方法。Briassoulis等[7]基于正交各向异性壳的拉伸刚度和弯曲刚度的一组解析表达式,对波纹壳进行了数值模拟。Sohrab等[8]提出一种新型的分层波纹复合芯,并通过实验进行了测试。Tian等[9]对波纹夹芯板进行了优化分析。Samanta等[10]首次提出了梯形波纹夹芯板的非线性几何分析,将波纹夹芯板等效成各向异性模型,对梯形波纹夹芯板进行了自由振动分析。Xia等[11]提出了一种基于均质化的波纹夹芯板模型,该模型可用于任何波纹形状。Li 等[12]针对铝制波纹夹芯板开展了空中爆炸试验研究和有限元数值分析,验证了有限元分析技术的可行性。王红霞等[13]和王青伟等[14]推导了考虑波纹拉伸变形的三角形波纹夹芯板的等效弹性参数,后来进行了修正。吴建均等[15]推导了泡沫填充下的三角形波纹夹芯梁的等效弹性常数公式,并且对泡沫波纹夹芯梁的模态进行实验研究和数值计算。还有一些学者对波纹夹芯板的结构性能、力学性能和冲击性能进行了研究[16-18]

    在夹芯板或板结构的研究中,发展了不同的理论,如Reissner板理论、基尔霍夫经典板理论(CLPT)及后来发展的各种剪切变形理论[19-21]等。Talha等[22]基于高阶剪切理论研究了梯度板的静态响应和自由振动。WU等[23]提出了基于RMVT的三阶剪切变形理论(TSDT)。THAI等[24]用正弦剪切变形理论(SSDT)分析了功能梯度板的弯曲、屈曲和振动特性。曹源等[25]用SSDT和修正的欧应力理论研究了功能梯度三明治微梁的静态弯曲和自由振动。但是,用这些理论来研究波纹夹芯板性能的还比较少。

    综上所述,波纹夹芯板具有很强的各向异性特性,目前多数文献研究四边简支边界条件下波纹夹芯板的动力学特性,但波纹夹芯板在实际应用中还有其它的边界条件,并且边界条件的影响较显著。鉴于此,本文将采用不同的夹层板理论研究波纹夹芯板在四边简支(SSSS)、四边固支(CCCC)、对边简支和固支(CCSS)、一边固支三边简支(CSSS)四种边界条件下的自由振动,与ABAQUS有限元仿真结果进行对比,验证理论模型的正确性,分析边界条件对波纹夹芯板振动特性的影响。此外,基于指数剪切变形理论(ESDT),讨论波纹夹芯板的材料参数和结构几何参数对系统振动特性的影响。所得结果为轻质波纹夹芯结构的优化设计提供了必要的理论指导。

    波纹夹芯板的模型如图1(a)所示,由上、下面板及中间的波纹芯层组成。在板中面建立x-y坐标系,z轴垂直于x-y面,z>0的一侧称为下表面,z<0的一侧称为上表面。波纹夹芯板的长度为a,宽度为b,高度为h,上、下板厚为hf图1(b)为波纹芯层的胞元,单胞的底边长为2p,波纹壁厚为tc,波纹与面板的夹角为θ,斜边长lc=p/cosθ芯层厚度hc=ptanθ

    在波纹夹芯板中,上、下面板采用各向同性均质体,中间波纹芯层等效为各向异性均质体,等效示意图如图2所示。仿照文献[13-15],考虑波纹夹芯板的伸缩变形,波纹芯层的等效参数表达式为

    E1(2)=EstcpsinθE2(2)=Estc3cosθhc3[1+(tchc)2cos2θ]G12(2)=Gsptcsinθhc2G13(2)=GstcsinθpG23(2)=Estcsin2θcosθhcv12(2)=vstc2cos2θ(hc2+tc2cos2θ)v21(2)=vsρ(2)=2ρstclcsin2θ (1)

    其中:E1(2)E2(2)G12(2)G13(2)G23(2)v12(2)v21(2)ρ(2)分别表示波纹芯层在各方向上的等效弹性模量、剪切模量、泊松比和密度;EsGsρs分别为基体材料的弹性模量、剪切模量和密度。

    图  1  波纹夹芯板的模型(a)和波纹单胞示意图(b)
    Figure  1.  Model diagrams of corrugated sandwich panel (a) and corrugated cell (b)
    a—Length of corrugated sandwich panel; b—Width of corrugated sandwich panel; lc—Length of the hypotenuse; hc—Height of core layer; tc—Wall thickness; θ—Corrugation angle; p—Length of bottom side
    图  2  波纹夹芯板等效示意图
    Figure  2.  Equivalent models of corrugated sandwich panel

    考虑到波纹夹芯板的横向剪切变形效应,位移场可表示为如下形式:

    u(x,y,z;t)=u0zw0x+f(z)ϕxv(x,y,z;t)=v0zw0y+f(z)ϕyw(x,y,z;t)=w0 (2)

    其中:u0v0w0分别为波纹夹芯板中面上任意一点的位移;ϕxϕy分别为波纹夹芯板的直法线沿x轴和y轴的转角;f(z)是决定横向剪切应力和应变沿厚度分布的形状函数。表1为几种不同剪切形状函数[19, 23-26]。CLPT不考虑横向剪切变形,低估了挠度,高估了固有频率和屈曲载荷,只适用于薄板,而一阶剪切变形理论(FSDT)在此基础上考虑了横向剪切变形,但是在上下表面处不满足面力自由的条件,需要剪切修正因子;ESDT、SSDT和TSDT都考虑了横向剪切变形,且在夹层板的上下表面处满足面力自由的条件,在计算中不需要横向剪切修正因子,很好地克服了CLPT和FSDT的局限性,三者的横向剪切应力和应变沿厚度的形状分别为指数函数型、正弦函数型和曲线型。

    表  1  不同板理论对应的剪切形状函数
    Table  1.  Shear shape functions corresponding to different plate theories
    Shear theoryFunction f (z)
    CLPT f(z)=0
    FSDT f(z)=z
    SSDT f(z)=hπsin(πzh)
    TSDT f(z)=z[143(zh)2]
    ESDT f(z)=ze2(zh)2
    Notes: CLPT—Classical plate theory; FSDT—First-order shear plate theory; SSDT—Sinusoidal shear deformation theory; TSDT—Third-order shear deformation theory; ESDT—Exponential shear deformation theory.
    下载: 导出CSV 
    | 显示表格

    根据小变形假设,位移-应变关系有:

    εxx=ux,εyy=vy,εzz=wz,γxz=uz+wx,γxy=uy+vx,γyz=vz+wy (3)

    将式(2)代入式(3)得到应变分量为

    {εxxεyyγxy}={εxx(0)εyy(0)γxy(0)}+z{εxx(1)εyy(1)γxy(1)}+f{εxx(3)εyy(3)γxy(3)},{γyzγxz}=f{γyz(2)γxz(2)},εzz=0 (4)

    其中,各应变分量的具体表达式为

    εxx(0)=u0x,εxx(1)=2w0x2,εxx(3)=ϕxx,εyy(0)=v0y,εyy(1)=2w0y2,εyy(3)=ϕyy,γxy(0)=u0y+v0x,γxy(1)=22w0xy,γxy(3)=ϕxy+ϕyx,γyz(2)=ϕy,γxz(2)=ϕx (5)

    波纹夹芯板的本构关系可表示为

    {σ(k)xxσ(k)yyτ(k)yzτ(k)xzτ(k)xy}=[Q(k)11Q(k)12000Q(k)21Q(k)2200000Q(k)4400000Q(k)5500000Q(k)66]{εxxεyyγyzγxzγxy} (6)

    其中,σ(k)xxσ(k)yyτ(k)yzτ(k)xzτ(k)xy为波纹夹芯板的应力和剪应力。

    各刚度系数可以表示为

    \begin{split} &Q_{11}^{(k)} = \frac{{E_1^{(k)}}}{{1 - \nu_{12}^{(k)}\nu_{21}^{(k)}}},Q_{12}^{(k)} = \frac{{E_1^{(k)}\nu_{21}^{(k)}}}{{1 - \nu_{12}^{(k)}ν_{21}^{(k)}}},Q_{22}^{(k)} = \frac{{E_2^{(k)}}}{{1 - \nu_{12}^{(k)}\nu_{21}^{(k)}}}, \\ &{Q_{66}} = {G_{12}},{Q_{44}} = {G_{23}},{Q_{55}} = {G_{13}},{Q_{21}} = {Q_{12}} \\[-12pt] \end{split} (7)

    其中:k=1、2、3 分别代表波纹夹芯板的上、中、下层;E1(k)E2(k)G12(k)G13(k)G23(k)ν12(k)ν21(k)分别表示上、下面板和芯层的弹性模量、剪切模量和泊松比。

    波纹夹芯板系统的势能、动能及外力势可以表示为

    \begin{split} {\rm{\delta}}U = &\int_0^a {\int_0^b {\int_{ - \frac{h}{2}}^{\frac{h}{2}} {({\sigma _{xx}}{\rm{\delta}}{\varepsilon _{xx}}} } } + {\sigma _{yy}}{\rm{\delta}}{\varepsilon _{yy}} + {\sigma _{{\textit{z}}{\textit{z}}}}{\rm{\delta}}{\varepsilon _{{\textit{z}}{\textit{z}}}} + {\tau _{y{\textit{z}}}}{\rm{\delta}}{\gamma _{y{\textit{z}}}} + \\ &{\tau _{x{\textit{z}}}}{\rm{\delta}}{\gamma _{x{\textit{z}}}} + {\tau _{xy}}{\rm{\delta}}{\gamma _{xy}}){\rm{d}}x{\rm{d}}y{\rm{d}}{\textit{z}} \\[-12pt] \end{split} (8)
    {\rm{\delta}}K = \int_0^a {\int_0^b {\int_{ - \frac{h}{2}}^{\frac{h}{2}} {\rho (\dot u{\rm{\delta}}\dot u + \dot v{\rm{\delta}}\dot v + \dot w{\rm{\delta}}\dot w)} } } {\rm{d}}x{\rm{d}}y{\rm{d}}{\textit{z}} (9)
    {\rm{\delta}}V = \int_0^a {\int_0^b {\int_{ - \frac{h}{2}}^{\frac{h}{2}} {q{\rm{\delta}}w{\rm{d}}x{\rm{d}}y{\rm{d}}{\textit{z}}} } } (10)

    其中:\dot u\dot v\dot w为波纹夹芯板在xy{\textit{z}}方向的运动速度;q为外载荷。

    根据哈密顿变分原理[27],得到波纹夹芯板系统的动力学方程为

    \begin{split} &\frac{{\partial {N_{xx}}}}{{\partial x}} + \frac{{\partial {N_{xy}}}}{{\partial y}} = {I_0}{{\ddot u}_0} - {I_1}\frac{{\partial {{\ddot w}_0}}}{{\partial x}}{\rm{ + }}{J_1}{{\ddot \phi }_x} \\ &\frac{{\partial {N_{yy}}}}{{\partial y}} + \frac{{\partial {N_{xy}}}}{{\partial x}} = {I_0}{{\ddot v}_0} - {I_1}\frac{{\partial {{\ddot w}_0}}}{{\partial y}}{\rm{ + }}{J_1}{{\ddot \phi }_y} \\ &\frac{{{\partial ^2}{M_{xx}}}}{{\partial {x^2}}} + 2\frac{{{\partial ^2}{M_{xy}}}}{{\partial x\partial y}} + \frac{{{\partial ^2}{M_{yy}}}}{{\partial {y^2}}} + q = {I_0}{{\ddot w}_0}{\rm{ + }}{I_1}\frac{{\partial {{\ddot u}_0}}}{{\partial x}}- \\ &{I_2}\frac{{{\partial ^2}{{\ddot w}_0}}}{{\partial {x^2}}} + {K_2}\frac{{\partial {{\ddot \phi }_x}}}{{\partial x}} + {I_1}\frac{{\partial {{\ddot v}_0}}}{{\partial y}} - {I_2}\frac{{{\partial ^2}{{\ddot w}_0}}}{{\partial {y^2}}} + {K_2}\frac{{\partial {{\ddot \phi }_y}}}{{\partial y}} \\ &\frac{{\partial {H_{xx}}}}{{\partial x}} + \frac{{\partial {H_{xy}}}}{{\partial y}} - {Q_x} = {J_1}{{\ddot u}_0} - {K_2}\frac{{\partial {{\ddot w}_0}}}{{\partial x}} + {J_2}{{\ddot \phi }_x} \\ &\frac{{\partial {H_{yy}}}}{{\partial y}} + \frac{{\partial {H_{xy}}}}{{\partial x}} - {Q_y} = {J_1}{{\ddot v}_0} - {K_2}\frac{{\partial {{\ddot w}_0}}}{{\partial y}} + {J_2}{{\ddot \phi }_y} \\ \end{split} (11)

    其中:

    \begin{array}{*{20}{l}} {\left[ {\begin{array}{*{20}{c}} {{N_{\xi \eta }}}\\ {{M_{\xi \eta }}}\\ {{H_{\xi \eta }}} \end{array}} \right] = \displaystyle\int_{ - \frac{h}{2}}^{\frac{h}{2}} {{\sigma _{\xi \eta }}} \left[ {\begin{array}{*{20}{c}} 1\\ {\textit{z}}\\ f \end{array}} \right]{\rm{d}}{\textit{z}},{Q_\xi } = \displaystyle\int_{ - \frac{h}{2}}^{\frac{h}{2}} {{\sigma _{\xi {\textit{z}}}}} f'{\rm{d}}{\textit{z}}}\\ {[{I_0},{I_1},{I_2},{J_1},{J_2},{K_2}] = \displaystyle\sum\limits_{k = 1}^3 {\int_{{\zeta _k}}^{{\zeta _{k + 1}}} {{\rho ^{(k)}}[1,{\textit{z}},{{\textit{z}}^2},f,{f^2},{\textit{z}}f]} } {\rm{d}}{\textit{z}}} \end{array} (12)

    其中,\xi \eta 可以用xy表示。

    将式(4)~(6)、式(12)代入式(11)得到位移形式的运动控制方程为

    {E_{i1}}{u_0} + {E_{i2}}{v_0} + {E_{i3}}{w_0} + {E_{i4}}{\phi _x} + {E_{i5}}{\phi _y} = 0,\; i = 1\sim5 (13)

    其中:

    {E_{11}} = {A_{11}}\frac{{{\partial ^2}}}{{\partial {x^2}}} + {A_{66}}\frac{{{\partial ^2}}}{{\partial {y^2}}} - {I_0}\frac{{{\partial ^2}}}{{\partial {t^2}}}
    {E_{22}} = {A_{22}}\frac{{{\partial ^2}}}{{\partial {y^2}}} + {A_{66}}\frac{{{\partial ^2}}}{{\partial {x^2}}} - {I_0}\frac{{{\partial ^2}}}{{\partial {t^2}}}
    {E_{12}}{\rm{ = }}{E_{21}} = ({A_{21}} + {A_{66}})\frac{{{\partial ^2}}}{{\partial x\partial y}}
    \begin{split} {E_{33}} =& - {G_{11}}\frac{{{\partial ^4}}}{{{x^4}}} - ({G_{12}} + {G_{21}} + 4{G_{66}})\frac{{{\partial ^4}}}{{\partial {x^2}\partial {y^2}}} - \\ &{G_{22}}\frac{{{\partial ^4}}}{{{y^4}}} + {I_2}{\nabla ^2}(\frac{{{\partial ^2}}}{{\partial {t^2}}}) - {I_0}\frac{{{\partial ^2}}}{{\partial {t^2}}} \\ \end{split}
    {E_{44}} = {R_{11}}\frac{{{\partial ^2}}}{{\partial {x^2}}} + {R_{66}}\frac{{{\partial ^2}}}{{\partial {y^2}}} + {V_{55}} - {J_2}\frac{{{\partial ^2}}}{{{t^2}}}
    {E_{55}} = {R_{22}}\frac{{{\partial ^2}}}{{\partial {y^2}}} + {R_{66}}\frac{{{\partial ^2}}}{{\partial {x^2}}} + {V_{44}} - {J_2}\frac{{{\partial ^2}}}{{\partial {t^2}}}
    {E_{13}} = {E_{31}} = {B_{11}}\frac{{{\partial ^3}}}{{{x^3}}} + ({B_{21}} + 2{B_{66}})\frac{{{\partial ^3}}}{{\partial x\partial {y^2}}} - {I_1}\frac{{{\partial ^3}}}{{\partial x\partial {t^2}}}
    {E_{14}} = {E_{41}} = {D_{11}}\frac{{{\partial ^2}}}{{\partial {x^2}}} + {D_{66}}\frac{{{\partial ^2}}}{{\partial {y^2}}} - {J_1}\frac{{{\partial ^2}}}{{\partial {t^2}}}
    {E_{15}} = {E_{51}} = {E_{24}} = {E_{42}} = ({D_{21}} + {D_{66}})\frac{{{\partial ^2}}}{{\partial x\partial y}}
    {E_{23}} = {E_{32}} = - {B_{22}}\frac{{{\partial ^3}}}{{\partial {y^3}}} - ({B_{21}} + 2{B_{66}})\frac{{{\partial ^2}}}{{\partial {x^2}\partial y}} + {I_1}\frac{{{\partial ^3}}}{{\partial y\partial {t^2}}}
    {E_{25}} = {E_{52}} = {D_{22}}\frac{{{\partial ^2}}}{{\partial {y^2}}} + {D_{66}}\frac{{{\partial ^2}}}{{\partial {x^2}}} - {J_1}\frac{{{\partial ^2}}}{{\partial {t^2}}}
    {E_{34}} = {E_{43}} = {L_{11}}\frac{{{\partial ^3}}}{{{x^3}}} + ({L_{21}} + 2{B_{66}})\frac{{{\partial ^3}}}{{\partial x\partial {y^2}}} - {K_2}\frac{{{\partial ^3}}}{{\partial x\partial {t^2}}}
    {E_{35}} = {E_{53}} = ({L_{12}} + 2{L_{66}})\frac{{{\partial ^3}}}{{\partial {x^2}\partial y}} + {L_{22}}\frac{{{\partial ^3}}}{{{y^3}}} - {K_2}\frac{{{\partial ^3}}}{{\partial y\partial {t^2}}}
    {E_{45}} = {E_{54}} = ({R_{11}} + {R_{66}})\frac{{{\partial ^2}}}{{\partial x\partial y}}
    \begin{split} &[{A_{ij}},{B_{ij}},{D_{ij}},{G_{ij}},{L_{ij}},{R_{ij}},{V_{ij}}] \\ &= \sum\limits_{k = 1}^3 {\int_{{\zeta _k}}^{{\zeta _{k + 1}}} {{Q^{(k)}}_{ij}[1,{\textit{z}},f,{{\textit{z}}^2},{\textit{z}}f} ,} {f^2},{(f')^2})]{\rm{d}}{\textit{z}} \end{split}

    假设位移分量为双三角函数,则{u_0}{v_0}{w_0}{\phi _x}{\phi _y}可表示为

    \begin{split} &\left\{ {{u_0},{\phi _x}} \right\} = \displaystyle\sum\limits_{m = 1}^\infty {\displaystyle\sum\limits_{n = 1}^\infty {\left\{ {{U_{mn}},{\Phi _{xmn}}} \right\}\frac{{\partial {X_m}(x)}}{{\partial x}}{Y_n}(y)} } {{\rm{e}}^{{\rm{i}}\omega t}}, \\ &\left\{ {{v_0},{\phi _y}} \right\} = \displaystyle\sum\limits_{m = 1}^\infty {\displaystyle\sum\limits_{n = 1}^\infty {\left\{ {{V_{mn}},{\Phi _{ymn}}} \right\}} } {X_m}(x)\frac{{\partial {Y_n}(y)}}{{\partial y}}{{\rm{e}}^{{\rm{i}}\omega t}}, \\ &\left\{ {{w_0}} \right\} = \displaystyle\sum\limits_{m = 1}^\infty {\displaystyle\sum\limits_{n = 1}^\infty {\left\{ {{W_{0mn}}} \right\}} } {X_m}(x){Y_n}(y){{\rm{e}}^{{\rm{i}}\omega t}} \end{split} (14)

    其中:{\rm{i}} = \sqrt { - 1} \omega 为波纹夹芯板系统自由振动下的固有频率。满足波纹夹芯板在4种边界条件下的位移分量形式可以用表2的函数表示。

    表  2  不同边界条件下的函数Xm(x) 和 Yn(y)
    Table  2.  Functions Xm(x) and Yn(y) for different boundary conditions
    Boundary conditionsFunction Xm(x)Function Yn(y)
    SSSS \sin \alpha x \sin \beta x
    CCCC 1 - \cos 2\alpha x 1 - \cos 2\beta x
    CCSS 1 - \cos 2\alpha x \sin \beta x
    CSSS \sin \alpha x(\cos \alpha x - 1) \sin \beta x
    Notes: SSSS—Four sides simply supported; CCCC—Four sides clamped; CCSS—Opposite sides simply supported and clamped; CSSS—One side fixed and three edges clamped; { {\alpha = m{\text{π}}} / a}; { {\beta = n{\text{π}} } / b}; m, n—Half-wave numbers in two orthogonal coordinate directions respectively.
    下载: 导出CSV 
    | 显示表格

    将式(14)代入式(13)可得系统的特征方程,简写为

    \left\{ {{{K}} - {\omega ^2}{{M}}} \right\}\left\{ {{\delta}} \right\} = 0 (15)

    其中:MK分别为波纹夹芯板系统的质量矩阵和刚度矩阵;{\left\{ {\bf{\delta }} \right\}^{\bf{T}}} = \left\{ {{U_{mn}},{V_{mn}},{\Phi _x}_{mn},{\Phi _y}_{mn},{W_{0mn}}} \right\}为系统的振动幅值。由于它们的取值是任意性的,因此令该特征方程的系数行列式为0,求解该代数方程,即可得到波纹夹芯板自由振动时的固有频率。

    根据以上理论模型,编写程序计算波纹夹芯板在不同板理论下的固有频率,并且与ABAQUS有限元仿真结果进行对比,验证理论模型的正确性。此外,计算了不同边界条件下波纹夹芯板的基频,分析边界条件对波纹夹芯板振动特性的影响。同时,研究在四种不同边界条件下波纹夹芯板材料参数及结构几何参数的变化对波纹夹芯板基频的影响。

    设波纹夹芯板的长a=240 mm,宽b=188.3 mm,上、下面板厚度hf=1 mm,波纹与面板的夹角θ=45°,波纹壁厚tc=1 mm,芯层厚度hc=8 mm。波纹夹芯板三层所采用的基体均为铝材料,其材料参数为:杨氏模量Es=71 GPa,泊松比νs=0.3,剪切模量Gs=Es/2(1+νs),密度ρs=2 810 kg/m3

    对波纹夹芯板系统进行无量纲化,无量纲化的频率可以定义为

    \varpi = \frac{{\omega {a^2}}}{h}\sqrt {\frac{{12{\rho _{\rm{s}}}(1 - \nu_{\rm{s}}^2)}}{{{E_{\rm{s}}}}}} (16)

    表3为5种不同板理论所求得的波纹夹芯板在四边简支边界条件下的前五阶固有频率。可以看出,采用SSDT、TSDT、ESDT理论所求得的固有频率与有限元误差较小,全部小于3%,FSDT由于需要剪切修正因子,所求结果误差比以上三个理论略偏大,CLPT由于未考虑横向剪切变形,高估了固有频率,所求结果相比其余4种剪切变形理论,误差要大很多。其中,在基频处,波纹夹芯板的运动和变形相对稳定,剪切应力对板变形的影响相对较小,因此在五种理论中,所求基频与ABAQUS有限元仿真相比误差较小。随着固有频率的增加,波纹夹芯板的变形越来越大,运动也愈加剧烈,因此剪切应力影响变大,考虑剪切变形且满足上下表面处面力自由的SSDT、TSDT和ESDT相对于CLPT和FSDT所求结果更准确。

    表  3  四边简支波纹夹芯板在不同理论下的固有频率理论解与有限元仿真结果
    Table  3.  Theoretical solutions and finite element simulation results of natural frequency of simply supported corrugated sandwich plates using different theories
    ModeABAQUSCLPTFSDTSSDTTSDTESDT
    ResultError/%ResultError/%ResultError/%ResultError/%ResultError/%
    (1,1) 31.18 31.72 1.75 31.41 0.77 31.00 −0.57 31.01 −0.54 30.99 −0.58
    (2,1) 65.39 69.52 6.32 68.09 4.13 65.82 0.66 65.88 0.75 65.79 0.61
    (1,2) 86.48 88.51 2.36 86.23 −0.29 83.74 −3.16 83.78 −3.12 83.74 −3.17
    (2,2) 116.13 125.70 8.24 121.21 4.38 115.60 −0.45 115.72 −0.35 115.57 −0.48
    (3,1) 118.46 132.06 11.48 127.11 7.30 119.24 0.66 119.45 0.84 119.12 0.56
    下载: 导出CSV 
    | 显示表格

    在四边简支边界条件下,波纹夹芯板前五阶振型模态如图3所示。

    图  3  波纹夹芯板前五阶振型图
    Figure  3.  The first five mode shapes of the corrugated sandwich plates

    在四种不同边界条件下,由不同板理论计算的波纹夹芯板在自由振动时的基频与有限元仿真结果如表4所示。可以看到,理论解与有限元仿真结果相比,CLPT由于忽略横向剪切应力导致所求结果稍微偏大,考虑横向剪切变形且满足上下表面处面力自由的SSDT、TSDT、ESDT所求结果比FSDT和CLPT的误差小。因为基频处波纹夹芯板的变形相对高频小,剪应力的影响有限,所以5种板理论所求结果误差都在工程允许的误差范围之内,由此也可验证四种边界条件下所假设的位移函数的正确性。比较四种边界条件下所得到的固有频率可以发现,波纹夹芯板在CCCC边界条件下的基频最大,SSSS边界条件下的基频最小,CCCC边界条件下的基频基本可以达到SSSS的1倍左右,CCSS和CSSS边界条件下的固有频率介于上述二者之间,并且两者相差较小,即四种边界条件下波纹夹芯板的基频的关系为CCCC>CCSS>CSSS>SSSS,由此可以得知,固支边界条件会使波纹夹芯板系统在自由振动时的基频增大。同样这也说明了波纹夹芯板边界的约束越多,系统结构整体刚度越大,导致整个系统频率特征值增大。因此,可以通过设置不同的边界条件来调整波纹夹芯板的固有振动频率。

    表  4  不同边界条件和板理论下波纹夹芯板的基频理论解与有限元仿真结果
    Table  4.  Theoretical solutions and finite element simulation results of fundamental frequency of corrugated sandwich plates with different boundary conditions and plate theories
    Boundary conditonsABAQUSCLPTFSDTSSDTTSDTESDT
    ResultError/%ResultError/%ResultError/%ResultError/%ResultError/%
    SSSS 31.18 31.72 1.75 31.41 0.77 31.00 −0.57 31.01 −0.54 30.99 −0.58
    CCCC 56.42 60.46 7.17 58.90 4.40 56.99 1.01 57.03 1.08 56.98 0.99
    CCSS 40.47 43.19 6.71 42.44 4.87 41.23 1.88 41.26 1.96 41.22 1.84
    CSSS 39.50 42.14 6.70 41.56 5.22 40.66 2.94 40.68 2.99 40.65 2.91
    下载: 导出CSV 
    | 显示表格

    4种不同边界条件下的波纹夹芯板的一阶振型模态如图4所示。

    图  4  不同边界条件下波纹夹芯板一阶振型图
    Figure  4.  The first mode shapes of corrugated sandwich plates under different boundary conditions

    波纹夹芯板的材料参数和结构几何参数对其振动有着重要的影响,通过进一步研究波纹夹芯板的振动特性,为其在工程应用方面提供足够的依据。本节将基于ESDT,研究四种不同边界条件下,波纹夹芯板材料参数和结构几何参数的变化对系统基频的影响。

    波纹夹芯板的上面板、下面板、波纹芯层选用不同的基体材料:Ti和Al,研究不同材料组合对波纹夹芯板固有频率的影响。Al的物理参数在前文已给出,Ti的材料参数为弹性模量Et=177 GPa,泊松比vt = 0.32,密度ρt=4 540 kg/m3。波纹夹芯板的组合方式为Ti-Al-Ti、Ti-Ti-Ti、Al-Al-Al和Al-Ti-Al。板的其它尺寸与上述算例一致,得到四种边界条件下不同材料组合的波纹夹芯板的基频如表5所示。可知,对于每一种边界条件,基于ESDT理论计算所得的四种材料组合下波纹夹芯板的基频大小依次为Ti-Al-Ti> Ti-Ti-Ti> Al-Al-Al> Al-Ti-Al,其中不同材料组合的频率在CCCC边界条件下变化稍大一些,但几种边界条件下的变化趋势基本一致。由式(15)可知,增大材料的弹性模量,即抗变形能力增强,波纹夹芯板结构的刚度增大,系统整体的频率会增大;增大材料的密度,波纹夹芯板的质量增大,波纹夹芯板的频率会降低,但对于波纹夹芯板的上、下面板,弹性模量的影响更显著;对于芯层,密度影响起主导作用。在工程应用中可以选取适当的材料组合以提高波纹夹芯板的固有频率。

    表  5  不同材料组合下波纹夹芯板的基频
    Table  5.  Fundamental frequencies of corrugated sandwich panels with different material combinations
    Boundary conditonAl-Al-AlTi-Ti-TiAl-Ti-AlTi-Al-Ti
    SSSS 30.99 38.72 29.07 40.53
    CCCC 56.98 71.16 54.31 71.99
    CCSS 41.22 51.46 39.96 52.38
    CSSS 40.65 50.76 39.03 52.17
    下载: 导出CSV 
    | 显示表格

    作为一种复合结构材料,波纹夹芯板的结构参数对其振动同样有着重要的影响,为了更好地观察波纹夹芯板的基频随结构几何参数的变化趋势,以下计算不再对系统固有频率进行无量纲化,波纹夹芯板各层采用的材料均为铝。

    保持波纹夹芯板的基本尺寸和芯层高度及总高度不变,波纹夹芯板在四种边界条件下的基频随波纹与面板夹角θ的变化如图5所示。可以看出,随着波纹与面板夹角θ的增大,在四种边界条件下,波纹夹芯板基频的变化趋势基本接近,都随着夹角θ的增大呈缓慢下降的趋势。由式(1)可知,波纹与面板夹角从30^\circ 变化到80^\circ 度时,芯层弹性模量E1和剪切模量G13增大,等效密度增大,其它等效参数变化相对较小,波纹夹芯板系统的刚度虽有一定的增大,但等效密度增大更明显,导致波纹夹芯板的基频呈下降趋势。另外,四种边界条件下,CCCC和SSSS边界条件下基频相差较大,且CCCC>SSSS;CSSS和CCSS边界条件下所得到的基频位于CCCC和SSSS之间,CCSS稍大于CSSS,但随着夹角的增大两者对应的波纹夹芯板的基频差值增大。波纹与面板的夹角θ越大,即波纹折皱密度越大,铝制波纹夹芯板越接近实体铝板。由此也可以得知,铝制波纹夹芯板的固有频率大于相同尺寸的实体铝板。

    图  5  波纹与面板夹角对波纹夹芯板基频的影响
    Figure  5.  Influence of the angle between corrugation and panel on the fundamental frequency of corrugated sandwich panel

    波纹芯层高度对波纹夹芯板基频的影响如图6所示。可知,随着芯层高度占比hc/h的增大,即芯层厚度增大,上、下面板厚度减小,4种边界条件下波纹夹芯板基频的变化趋势基本接近。由式(1)可知,随着波纹芯层高度hc的增大,波纹的结构参数(斜边长lc、半底边长p)增大,波纹芯层各个方向的弹性模量和剪切模量减小,导致系统的刚度减小,从而使基频降低,但是随着芯层高度占比hc/h的增大,波纹芯层的等效密度减小,使系统基频增大。因为在hc/h≤0.8时芯层等效密度的影响起主导作用,之后弹性模量和剪切模量的影响起主导作用,所以导致波纹夹芯板的基频先增大后减小。在hc/h=0.8附近,基频达到最大值,在hc/h>0.8时,波纹夹芯板的基频迅速下降。因此可以得知,在实际工程应用中选取适当的芯层占比可以提高波纹夹芯板的固有频率。

    图  6  波纹芯层高度占比对波纹夹芯板基频的影响
    Figure  6.  Influence of corrugated core height ratio on the fundamental frequency of corrugated sandwich panel

    波纹夹芯板的基频随波纹壁厚的变化如图7所示。由等效参数计算式(1),随着壁厚的增加,波纹芯层的剪切模量和弹性模量增大,且E12呈直线增大,系统刚度增大,同样芯层的等效密度也呈直线增大,导致系统的基频减小。因为等效密度的影响起主导作用,所以波纹夹芯板的基频持续减小。另外,CCSS和CSSS两种边界条件下的基频的差值略微增大,且4种边界条件下,CCCC边界条件下波纹夹芯板的基频相对于其他3种边界条件在壁厚tc≤3 mm时下降速度略快一些,其余边界条件下,波纹夹芯板基频的下降趋势基本一致。

    图  7  波纹壁厚度对波纹夹芯板基频的影响
    Figure  7.  Influence of corrugated wall thickness on the fundamental frequency of corrugated sandwich panel

    波纹夹芯板厚度 h对波纹夹芯板基频的影响如图8所示。可见,波纹夹芯板芯层在各方向的弹性模量和剪切模量在h≤30时迅速减小,芯层刚度随之减小,之后几乎保持不变,导致系统的固有频率减小。但是由式(1)可知,芯层的等效密度同样在h≤30时迅速减小,之后几乎保持不变,且等效密度的影响起着主导作用。当波纹夹芯板的总厚度h<30 mm时,四种边界条件下波纹夹芯板系统的基频呈现明显增大的趋势,CCCC边界条件下的基频增长速率最快,CSSS和CCSS边界条件所对应的基频曲线接近重合,在h=15 mm附近CSSS条件下所求的基频开始高于CCSS边界条件下所求的基频。当h>30 mm时,四条曲线都趋于平稳,波纹夹芯板基频变化波动很小,此时板的宽厚比b/h<6,波纹夹芯板由薄板逐渐变为厚板。根据以上分析可以得知,在工程应用中适当提高波纹夹芯板的厚度可以提高系统的固有频率。

    图  8  波纹夹芯板厚度h对波纹夹芯板基频的影响
    Figure  8.  Influence of corrugated plate thickness on the fundamental frequency of corrugated sandwich panel

    k为变化比例因子,将波纹夹芯板结构的所有几何尺寸分别乘以比例因子k,即波纹夹芯板结构整体变大或者缩小,得到的波纹夹芯板基频的变化曲线如图9所示。随着k的变化,波纹夹芯板芯层的弹性模量、剪切模量和密度保持不变。由于波纹夹芯板长和宽的增大,导致整个系统质量增加,因此系统的固有频率将减小。图中所取变化比例因子k为0.2~3,四种边界下波纹夹芯板的基频在k\!\leqslant\!1时急剧下降,CCSS和CSSS曲线基本重合;在k \!\geqslant\!1时,四种边界条件下的波纹夹芯板系统的基频越来越接近。由此可知,当波纹夹芯板尺寸无限大时,四种边界条件下波纹夹芯板系统的基频会接近相等,且波纹夹芯板尺寸越大系统的基频就越小。

    图  9  比例因子k对波纹夹芯板基频的影响
    Figure  9.  Influence of scale factor on the fundamental frequency of corrugated sandwich panel

    研究了波纹夹芯板在四种边界条件下的自由振动特性,对比了不同板理论所求得的固有频率,并与有限元仿真结果进行了对比。此外,基于指数剪切变形理论(ESDT)分析了波纹夹芯板材料参数和结构几何参数的变化对系统固有频率的影响。

    (1)对于基尔霍夫经典板理论(CLPT)、一阶剪切变形理论(FSDT)、正弦剪切变形理论(SSDT)、三阶剪切变形理论(TSDT)、ESDT五种板理论,其中CLPT由于不考虑板的横向剪切变形,因此求得系统自由振动的固有频率误差最大,FSDT所求固有频率次之,SSDT、TSDT、ESDT所求固有频率相近,且与有限元仿真结果相比,误差最小。

    (2)四种边界条件下波纹夹芯板自由振动的基频大小依次为:四边固支(CCCC)>对边简支和固支(CCSS)>一边固支三边简支(CSSS)>四边简支(SSSS),且CCCC的基频比SSSS的基频约大1倍, 即波纹夹芯板结构的边界约束越多,系统的固有频率越大。

    (3)增大波纹夹芯板材料的弹性模量会导致其刚度变大,进而使系统的基频增大;增大材料密度会导致波纹夹芯板的质量增大,进而使系统的基频减小,对于上、下面板,弹性模量的影响较显著,而对于夹芯层,密度的影响起主导作用。

    (4)波纹夹芯板的结构几何参数对系统的振动有着重要影响。随着波纹与面板的夹角\theta 或波纹壁厚tc的增大,波纹夹芯板的基频变小;随着芯层占比hc/h的增大,波纹夹芯板的基频先增大后减小;保持hc/h、面板占比hf/h不变,随着波纹夹芯板厚度h的增大,波纹夹芯板的基频增大明显;随着波纹夹芯板尺寸的增大其基频下降,且四种边界条件下波纹夹芯板的基频趋近相等。

  • 图  1   粗骨料粒径级配

    Figure  1.   Grading curves of various coarse aggregates

    图  2   试验装置

    F—Load

    Figure  2.   Test setup

    图  3   再生砖混骨料混凝土抗压强度

    Figure  3.   Compressive strength of mixed recycled aggregate concrete

    图  4   再生砖混骨料混凝土抗压试验破坏形态

    RBA—Recycled brick aggregate; RCA—Recycled concrete aggregate

    Figure  4.   Failure modes of mixed recycled aggregate concrete comperessive test

    图  5   再生砖混骨料混凝土劈裂抗拉强度

    Figure  5.   Splitting tensile strength of mixed recycled aggregate concrete

    图  6   再生砖混骨料混凝土劈裂抗拉试验破坏形态

    Figure  6.   Failure modes of mixed recycled aggregate concrete splitting tensile test

    图  7   再生砖混骨料混凝土抗折强度

    Figure  7.   Flexural strength of mixed recycled aggregate concrete

    图  8   再生砖混骨料混凝土抗折试验破坏形态

    Figure  8.   Failure modes of mixed recycled aggregate concrete flexural test

    图  9   RBA的界面模型

    ITZ—Interfacial transition zone

    Figure  9.   Interface mode of RBA

    图  10   再生砖骨料-砂浆界面过渡区(ITZ)的SEM图像

    CH—Calcium hydroxide; Aft—Ettringite; C-S-H—Hydrated calcium silicate

    Figure  10.   SEM images of ITZ between recycled brick aggregate and mortar

    图  11   再生砖混骨料混凝土典型应力-应变曲线

    fc—Peak stress; εc—Peak strain

    Figure  11.   Typical stress-strain curve of mixed recycled concrete

    图  12   再生砖混骨料混凝土轴心受压破坏形态

    Figure  12.   Failure mode of axial compression of mixed recycled concrete

    图  13   再生砖混骨料混凝土单轴受压应力-应变曲线

    σ—Stress; ε—Strain

    Figure  13.   Stress-strain curves of mixed recycled aggregate concrete under uniaxial compression

    图  14   再生砖混骨料混凝土峰值应力与峰值应变

    Figure  14.   Peak stress and peak strain of mixed recycled concrete

    图  15   再生砖混骨料混凝土弹性模量及其试验值和计算值之比

    Figure  15.   Modulus of elasticity and ratio of test value to calculated value of mixed recycled concrete

    图  16   无量纲化和拟合再生砖混骨料混凝土单轴受压本构曲线

    Figure  16.   Dimensionless and fitting constitutive curves of mixed recycled aggregate concrete under uniaxial compression

    图  17   再生砖混骨料混凝土试验曲线与拟合曲线对比

    Figure  17.   Comparing test curve and the fitting curve of mixed recycled aggregate concrete

    图  18   再生砖混骨料混凝土各力学性能换算公式

    Figure  18.   Conversion formula of mechanical properties of mixed recycled aggregate concrete

    表  1   砖骨料(RBA)、再生混凝土骨料(RCA)及天然骨料(NA)的物理性能

    Table  1   Properties of recycled brick aggregate (RBA), recycled concrete aggregate (RCA) and natural aggregate (NA)

    TypeStacking density/(kg·m−3)Apparent density/(kg·m−3)Crush index/%Water absorption/%
    24 h3 d
    RBA 890169722.420.321.7
    RCA14502693 9.8 3.5 3.6
    NA15502780 7.2 1.2
    下载: 导出CSV

    表  2   再生砖混骨料混凝土配合比

    Table  2   Mix proportion of mixed recycled aggregate concrete

    Samplew/bWater/
    (kg·m−3)
    Cement/
    (kg·m−3)
    Sand/
    (kg·m−3)
    NA/
    (kg·m−3)
    RCA/
    (kg·m−3)
    RBA/
    (kg·m−3)
    Water reducer/%
    NC(0.3) 0.3 138 460 570 1150 0 0 1.2
    0%RBC(0.3) 138 460 570 0 1120 0
    50%RBC(0.3) 138 460 570 0 560 350
    100%RBC(0.3) 138 460 570 0 0 700
    NC(0.4) 0.4 185 460 570 1150 0 0 0.5
    0%RBC(0.4) 185 460 570 570 1120 0
    50%RBC(0.4) 185 460 570 0 560 350
    100%RBC(0.4) 185 460 570 0 0 700
    Notes: NC—Natural aggregate concrete; RBC—Mixed recycled aggregate concrete; w/b—Water cement ratio; The numbers 0%, 50% and 100% represent the volume replacement rate of brick aggregate in recycled aggregate, respectively.
    下载: 导出CSV

    表  3   再生砖混骨料混凝土轴心受压试验主要试验结果

    Table  3   Main test results of mixed recycled concrete axial compression test

    SamplePeak stress
    {\mathit{f}}_{\mathbf{c}} /MPa
    Peak strain
    {\mathbf{\varepsilon }}_{\mathbf{c}}/ {10}^{-3}
    Ascending portion 0.4 {\mathit{f}}_{\mathbf{c}} Strain of 0.4 {\mathit{f}}_{\mathbf{c}} Elastic
    modulus/GPa
    Descending
    portion 0.85 {\mathit{f}}_{\mathbf{c}}
    Peak strain
    of 0.85 {\mathit{f}}_{\mathbf{c}}
    NC(0.3)38.601.25315.310.49131.1832.811.321
    0%RBC(0.3)35.481.27714.190.50727.9930.161.385
    50%RBC(0.3)30.892.24212.360.89413.8326.262.352
    100%RBC(0.3)27.722.41311.091.04110.6523.562.518
    NC(0.4)35.631.50714.250.48329.5030.291.647
    0%RBC(0.4)33.801.57113.520.63121.4328.731.662
    50%RBC(0.4)29.612.17411.840.88413.3925.172.264
    100%RBC(0.4)26.352.56110.541.137 9.2722.392.679
    下载: 导出CSV

    表  4   再生砖混骨料混凝土弹性模量计算值与试验值

    Table  4   Calculated and experimental values of elastic modulus of mixed recycled concrete

    SampleTest value/
    GPa
    {\mathit{f} }_{\mathbf{c}\mathbf{u}}
    /MPa
    Calculated value/GPaRatio
    NC(0.3)31.1847.934.190.912
    0%RBC(0.3)27.9941.532.940.850
    50%RBC(0.3)13.8336.731.460.439
    100%RBC(0.3)10.6533.630.930.344
    NC(0.4)29.5042.633.170.889
    0%RBC(0.4)21.4336.231.660.677
    50%RBC(0.4)13.3932.530.600.437
    100%RBC(0.4) 9.2730.429.930.311
    Note: fcu—Compressive strength.
    下载: 导出CSV

    表  5   再生砖混骨料混凝土本构参数ab

    Table  5   Constitutive parameters a and b of mixed recycled aggregate concrete

    SampleParameter of aParameter of b
    Fitting parameterVariation/%Fitting parameterVariation/%
    NC 0.361 0.00 31.301 0.00
    0%RBC 0.463 28.25 54.505 74.13
    50%RBC 0.222 −38.50 60.624 93.68
    100%RBC 0.018 −95.01 71.659 128.94
    下载: 导出CSV
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    其他类型引用(5)

  • 目的 

    废弃粘土砖块约占我国建筑垃圾总量的30%~50%,其往往与废弃混凝土混杂在一起难以分离。现有研究表明将废弃混凝土块和废弃黏土砖块一同破碎后作为再生砖和再生混凝土混合再生粗骨料使用是可行的,但是再生砖混骨料混凝土的材料性能及其设计方法目前尚未统一,这严重阻碍了此类再生混凝土的工程应用。本文研究了再生砖混骨料混凝土的基本力学性能与单轴应力-应变关系,并通过对过镇海本构模型进行修正,提出了一个可用于对此类再生混凝土进行结构分析与设计的本构模型。

    方法 

    以不同水胶比(0.3和0.4)、不同再生骨料取代率(体积法取代0%、50%、100%)为控制参数配置混凝土。在配置时先将细骨料和水泥在搅拌机中混合搅拌2min。然后加入粗骨料,搅拌2min后再加入水和少许减水剂,搅拌1min。测试搅拌均匀的混凝土拌合物的坍落度,若不满足则加入少许减水剂继续搅拌,重复至坍落度达到试验要求。将调制好的混凝土制作为18个立方体(100mm×100mm×100mm)和18个棱柱(100mm×100mm×400mm)用以测试混凝土试块的抗压强度,劈裂抗拉强度,抗折强度以及进行单轴压缩应力-应变全曲线试验。试块在室内养护1d后拆模,移入养护箱中继续养护,养护条件设定为标准养护条件(T=(20±2)℃,RH≥95%)。以试验数据为基础提出再生砖混骨料混凝土力学性能换算公式,并通过修正过镇海本构模型,建立再生砖混骨料混凝土单轴受压本构模型。

    结果 

    与天然骨料混凝土相比,不同配合比再生混凝土力学性能有不同程度的下降,其中随着再生砖骨料含量的增加,其力学性能下降较为显著,与对照组相比,全再生砖骨料混凝土的抗压、劈裂抗拉和抗折强度分别下降了29.9%、28.5%和15.56%。掺砖骨料混凝土的峰值应变明显增加,且弹性模量显著降低。观察各试块的破坏形态发现,几乎所有砖骨料呈断裂形态,黏结砖骨料的水泥胶界面并未裂开。对于砖混再生骨料混凝土,黏结再生混凝土骨料的水泥胶界面和砖骨料同时开裂,但再生混凝土骨料大部分并未开裂。再生砖混骨料混凝土的劈裂抗拉强度、抗折强度、峰值应力、峰值应变与其抗压强度均表现出较强的相关性.

    结论 

    再生砖骨料的高吸水性与高孔隙率造成的薄弱区域对混凝土力学性能有重要影响,再生砖混骨料混凝土脆性指数明显高于普通混凝土。砖骨料与再生混凝土骨料的老砂浆-新砂浆界面过渡区强度低是导致试块抗压强度降低的主要原因。砖骨料替代率达到100%时抗压强度下降高达29.9%,但是仍能保证一定的力学性能储备。对试验结果进行了拟合,得到了再生砖混骨料混凝土力学性能换算关系。建立了再生砖混骨料混凝土单轴受压本构模型,为此类再生混凝土的理论模型研究提供参考。

  • 废弃粘土砖块约占我国建筑垃圾总量的30%~50%,其往往与废弃混凝土混杂在一起难以分离。现有研究表明将废弃混凝土块和废弃黏土砖块一同破碎后作为再生砖和再生混凝土混合再生粗骨料使用是可行的,但是再生砖混骨料混凝土的材料性能及其设计方法目前尚未统一,这严重阻碍了此类再生混凝土的工程应用。

    本文配制了0.3和0.4两种水胶比情况下的对照混凝土(只含天然粗骨料)和不同取代率情况下的再生砖混骨料混凝土(100%再生混凝土骨料,100%再生砖骨料和50%再生混凝土骨料+50%再生砖骨料)。研究了不同配合比试块的立方体抗压、劈裂抗拉和抗折强度,以及应力-应变关系等内容。根据试验数据建立了再生砖混骨料混凝土单轴受压本构模型与再生砖混骨料混凝土力学性能换算公式,为此类再生混凝土材料的设计与应用提供参考。

    砖混再生混凝基本土力学性能

    再生砖混骨料混凝土各力学性能换算公式

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出版历程
  • 收稿日期:  2023-04-05
  • 修回日期:  2023-05-14
  • 录用日期:  2023-05-24
  • 网络出版日期:  2023-05-31
  • 刊出日期:  2024-01-31

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